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[Articles Home]  [Add Article]  

Bandwidth versus Keying Speed

Mickey Cox (K5MC) on May 26, 2007
View comments about this article!


Bandwidth versus Keying Speed

Introduction

A popular article on this reflector says that it is a "misconception" that the "bandwidth" of a CW transmitter is a function of the keying speed. On the other hand, The ARRL Handbook says that the keying speed is a factor in determining the bandwidth "occupied" by a CW signal. What's going on here?

Although there are a variety of potential pitfalls when discussing this topic, the most obvious one is the meaning of the word "bandwidth" itself. Many definitions of bandwidth exist and it is important that the precise definition or type of signal bandwidth be made clear early on.

Fourier Analysis of Signals

I will focus here on the "power" bandwidth of a CW transmitter when keyed by a long string of dits. According to Couch [1], the power bandwidth is f2 - f1, where f1 < f < f2 defines the frequency band in which 99% of the total average power resides. Note that this definition is similar to the FCC's definition of "occupied" bandwidth:

Occupied bandwidth. The frequency bandwidth such that, below its lower and above its upper frequency limits, the mean powers radiated are each equal to 0.5 percent of the total mean power radiated by a given emission [2].

In studying the specific waveforms presented here, I have used classical Fourier analysis as described in practically all of the communication systems and signal analysis textbooks written over the past 50 years or more.

Let's start with a very good keying wave shape, a sinusoidal-shaped pulse with identical rise and fall times of 5 milliseconds as shown in Figure 1. Now let's assume we form a periodic signal using these shaped pulses with a duty cycle of 50% to represent a long string of dits. Since we want to maintain the same rise/fall characteristics (shapes and times) regardless of speed, we will only vary the time duration of the constant amplitude portion of each pulse (designated as tc) to increase or decrease the number of dits sent per second. I have chosen two specific speeds here, 2.4 words per minute (wpm) and 30 wpm. These speeds were convenient choices mathematically and are also considered to be reasonably representative of the speed range employed by many hams. The value of tc is 0.490 seconds and 0.030 seconds for 2.4 wpm and 30 wpm, respectively. (These values of tc were found by first determining that the number of dits per second is 1 and 12.5 for 2.4 wpm and 30 wpm, respectively.)

Once the exact keying waveform has been decided, the detailed Fourier analysis can begin. If a periodic pulse signal is assumed for the keying waveform, one can calculate its Fourier series and the resulting average power (on a 1-ohm basis) for each discrete frequency component. Once the frequency characteristics of the keying waveform (which is the modulating signal) are known, the frequency characteristics of the radiated CW signal (which, mathematically, is binary ASK) can be found via trigonometric identities because the output signal is the product of the modulating signal and the high frequency carrier.

It turns out that the 99.1% power bandwidth of the 2.4-wpm CW/ASK signal is 34 Hz for the 5-ms sinusoidal-shaped keying waveform. (That is, 99.1% of the total power in the 2.4-wpm CW signal is contained by the carrier and the first 17 sideband pairs.) However, the 99.1% power bandwidth of the 30-wpm CW signal is 150 Hz. (99.1% of the total power in the 30-wpm CW signal is contained by the carrier and the first 6 sideband pairs.) Even though both signals have exactly the same rise and fall characteristics, Fourier analysis indicates that the 99.1% power bandwidth of the 30-wpm CW signal is over four times as large as that of the 2.4-wpm signal!

0x01 graphic

Figure 1. Sinusoidal keying waveform with symmetrical rise and fall times

Now suppose our keying waveform is changed from the very good one described above to one having zero rise and fall times. "Square-wave" keying is quite a bit easier to examine mathematically than sinusoidal keying and it will yield a "worst-case" value of power bandwidth for a given speed. As before, the speed of the dits is set so that we are sending at a rate of either 2.4 wpm or 30 wpm. In the case of square-wave keying, the 99.1% power bandwidth for our CW signal is 42 Hz and 525 Hz when sending dits at 2.4 wpm and 30 wpm, respectively. Once again we see that the power bandwidth increases significantly in going from 2.4 to 30 wpm. In fact, since both the rise and fall times of this keying waveform are zero, the power bandwidth ratio will be exactly equal to the speed ratio (12.5 to 1 in this specific example). Of course, we also expected the power bandwidth to increase significantly in going from sinusoidal keying to square-wave keying at the same speed. At 2.4 wpm, the 99.1% power bandwidth ratio is 1.24 for the two keying waveforms, but at 30 wpm the ratio is a whopping 3.50. The results are summarized in Table 1 below.

2.4 words per minute

30 words per minute

Sinusoidal keying (5 ms)

34 Hz

150 Hz

Square-wave keying

42 Hz

525 Hz

Table 1. 99.1% power bandwidth for CW/ASK transmitter for periodic signaling

I have purposely avoided cluttering this article with the mathematical details used to obtain the values shown in Table 1. If anyone is interested, I will be glad to post the details in a follow-up article or via email. Although I have carefully checked all of my calculations, in some cases by both time-domain and frequency-domain approaches, there is always the possibility of some computational errors. However, these answers appear to be quite consistent with my expectations and with such sources as The ARRL Handbook.

Summary

The concept of "bandwidth" commonly used in electrical engineering (and certainly used by the FCC in its definition of occupied bandwidth) is a "time averaged" quantity. As shown in Table 1, 99.1% of the total mean (average) power of the 30-wpm signal resides in a wider bandwidth as compared to the 2.4-wpm signal. A crucial point to be made here is that the concept of occupied bandwidth does not say that the strength of the individual key clicks generated by a poorly designed transmitter is reduced when the sending speed is decreased! The information provided by the occupied bandwidth is exactly that described in its definition. In closing, however, I do want to point out that if I have to be subjected to key clicks when operating CW, I would much prefer that the offending transmitter send at a speed of 1 word per 20 minutes rather than 20 words per minute!

References

[1] Leon W. Couch, Digital and Analog Communication Systems, 7th ed., Pearson

Prentice Hall, 2007.

[2] FCC Rules and Regulations, 47 CFR 2.202

Member Comments:
This article has expired. No more comments may be added.
 
Bandwidth versus Keying Speed  
by SM0AOM on May 26, 2007 Mail this to a friend!
By a substantially identical reasoning, the ITU/CCIR
once formulated the "necessary bandwidth" formulas
in the Radio Regulations.

For A1A emission or "on/off telegraphy" it reads

Bn = BK

where Bn = necessary bandwidth in Hz
B = keying speed in Bauds
K = factor to accommodate the number of keying sidebands necessary to recreate the shapes of the signal elements. K is usually assumed to be 3 for
"non-fading circuits" or "soft keying", 5 for
"fading circuits" or "hard keying"
It is further assumed that the keying envelope functions are close to optimal.

Using the above formula,
a 20 WPM (16,66 Baud) A1A signal has a necessary bandwidth of 84 Hz for "hard keying" and 50 Hz for "soft keying".

For an in-depth discussion by W9CF of the optimum keying envelope function see
http://fermi.la.asu.edu/w9cf/articles/click/index.html

73/

Karl-Arne
SM0AOM


 
RE: Bandwidth versus Keying Speed  
by W6TH on May 26, 2007 Mail this to a friend!
.
Very interesting.

Bandwidth versus Keying Speed versus my 250 Hz cw Filter.

Very interesting.

W6TH

.:
 
Bandwidth versus Keying Speed  
by N0CTI on May 26, 2007 Mail this to a friend!
Looking at the results in the table I conclude that bandwidth is used more efficiently with soft keying rather than hard keying. Also, with hard keying the bandwidth per word-per-minute is constant; bandwidth is directly proportional to speed. With soft keying, faster speeds use bandwidth more efficiently than slow speeds.

Interesting. Thanks for the article.

Dave K0DCH (eham database is not quite up to date.)
 
RE: Bandwidth versus Keying Speed  
by N4DSP on May 26, 2007 Mail this to a friend!
Congratulations to eHam and the authors of these articles. Its about time. Great learning experience for all. Who said there are no longer any elmers.

73
john-n4dsp
 
Bandwidth versus Keying Speed  
by W8AD on May 26, 2007 Mail this to a friend!

This a great informative article. This is the kind of thing we need on E-HAM. The quality of this article should encourage hams, both new and experienced, that there are very knowledgeable and nice folks out there who make this a great hobby!

Thank you,

Don, W8AD (hope the trolls stay under the bridge on this one!)
 
RE: Bandwidth versus Keying Speed  
by N6XL on May 26, 2007 Mail this to a friend!
OUT-STANDING, we could use more articles like this.

73's
Paul
 
RE: Bandwidth versus Keying Speed  
by W6TH on May 26, 2007 Mail this to a friend!
.
K5MC Mickey,

"Quote Mickey"

In closing, however, I do want to point out that if I have to be subjected to key clicks when operating CW, I would much prefer that the offending transmitter send at a speed of 1 word per 20 minutes rather than 20 words per minute!
................................................

Well my friend, back in the "old days", key clicks never bothered us and speeds were well above 35 wpm just using a bug. Believe me with a few hundred volts across our bugs many time caused key clicks just keying the cathodes of the crystal oscillators. So I say the key clicks never was a problem.

We, back then, wanted very hard keying and not the soft kind as at the softer, higher speeds, (50 wpm) the words were run much closer together and sounded as though there were no spacing. Another thing we copied by the sound of the words and not by characters as is taught today.

So all in all, I still enjoy the hard keying and especially at speeds at 50 and above for nice copy, regardless of key clicks or not.

It was very easy to soften the cw as all we did was to put a 100 ohm resistor in series with the bug and a 1 Mfd capacitor across the resistor and go lower until the op on the other enjoyed the sound.

Key clicks were told to the operator and he worked on the keying until all was accomplished.

Nice article Mickey and hope we get more to elmer the new Amateur Radio Operators, but remember old days used logic and were creative.Now, "Thats Brother Hood".

73, W6TH
.:
 
RE: Bandwidth versus Keying Speed  
by W7ETA on May 26, 2007 Mail this to a friend!
Wow!

A three fer: great prose, coherent, and concise.

Thanks

73
Bob
 
Bandwidth versus Keying Speed  
by K6YE on May 26, 2007 Mail this to a friend!
Mickey,

I echo the other posts. Great article!!!

Semper Fi,

Tommy - K6YE
DX IS
 
RE: Bandwidth versus Keying Speed  
by W8JI on May 26, 2007 Mail this to a friend!
Hi Mickey,

nice article but the bandwidth is actually set by the rise and fall times and shapes, not by the keying speed.

The keying speed only controls the number of times the offending sidebands repeat.

You can see detailed explanations of this on my web page at:

http://www.w8ji.com/keyclicks.htm

This page includes links to W9CF's site and a page with a white paper by Mark Amos.

73 Tom

 
RE: Bandwidth versus Keying Speed  
by W8JI on May 26, 2007 Mail this to a friend!
By the way, most important is the link to W9CF's website where he shows the power distribution of keyclicks (the sidebands) of a CW signal.

Link:

http://fermi.la.asu.edu/w9cf/articles/click/index.html

If you look at the bandwidth distribution you will find the overall shape of the sidebands (attenuation vs. frequency as you tune off higher or lower) is identical with all keying speeds. The only thing that happens is nulls and peaks move around inside that overall shape, but the receiver doesn't know the difference since its filter always has to be wide enough to pass all the sidebands.

The W9CF and other pages and papers dispell the common misconception that overall bandwidth changes with speed. The badwidth ALWAYS has to be wide enough to pass the rising and falling edges of the envelope.

73 Tom
 
RE: Bandwidth versus Keying Speed  
by AA4PB on May 26, 2007 Mail this to a friend!
Tom, is that because the keying speed on any normal CW signal is slow enough that the shape of the rise and fall times is the major contributor to bandwidth? As the speed countinues to rise (as in 300 baud, for example) then the speed becomes a major contributor to bandwidth? Otherwise it seems that we could run some very high baud rates on HF without worrying about occupied bandwidth.
 
RE: Bandwidth versus Keying Speed  
by W6TH on May 26, 2007 Mail this to a friend!
.
Not much to really discuss on this post because there are two types of key clicks that I remember...One type that was within a few Hz of center frequency and the other type that was up and down the center frequency a few Khz.

Another, we may call it a third one was using a RF amplifier and was caused by poor neutralization of the final amplifier.

I enjoy the keying of a very fast rise time and a slower falloff time, guess it is up to the receiver and the human ear as many have looked good on the osciloscope and yet did not seem to sound so good.

Radios of today are as close as one can get as the majority sound exceptionally good.The outboard keyers also do help the keying even with a different dot to dash ratio.Then again most say the semi breakin sounds better than the full breakin.

..............................Tasters Choice.........

.:
 
RE: Bandwidth versus Keying Speed  
by KE3HO on May 26, 2007 Mail this to a friend!
<<< "is that because the keying speed on any normal CW signal is slow enough that the shape of the rise and fall times is the major contributor to bandwidth?" >>>

Look at it this way: Consider Figure 1 above. The CW keying waveform as shown has three parts, the rise time, the period where the RF output is constant (tc), and the fall time.

During the rise time, the RF output is a time varying signal - in other words, it is a modulated signal. This time-changing signal produces sidebands. The sidebands produced are determined solely by the rise time and the shape of the keying function during the rise time.

During the "tc" period, the RF output is constant - in other words, it is a pure unmodulated carrier. During this period no sidebands are produced. The width of the carrier is set by the stability of the rigs oscillator, power supply stability, etc.

During the fall time, once again the signal is time-varying, so once again sidebands are produced.

How does keying speed play into this? Consider the rise time period. The keying waveform and the rise time are fixed - they do not depend on keying speed. If you don't believe this, they ask yourself the following question: "When I put down the key, how does the rig know how long I am going to hold it down?" See what I am saying? The only way that the rise time and keying waveform could change with keying speed would be if the rig somehow knew how long you were going to hold down the key. It can't. Period. Same goes for the fall time. The fall time and keying waveform are fixed.

Looking at the waveform again, as keying speed increases, the only thing that changes is the middle period, tc. As keying speed increases, tc becomes shorter. However, this is the period where the rig is producing as close to a pure unmodulated carrier as it can. The rise time period and fall time period are not affected by keying speed, so the sidebands that they produce do not change with keying speed.

73 - Jim
 
RE: Bandwidth versus Keying Speed  
by W8JI on May 26, 2007 Mail this to a friend!
by AA4PB on May 26, 2007 Tom, is that because the keying speed on any normal CW signal is slow enough that the shape of the rise and fall times is the major contributor to bandwidth? >>

Picture it this way. When we key the transmitter the waveshape of the envelope changes. That waveshape has a rise time and a fall time, and a slope rate within that time.

With a perfect sine shaped rise and fall time each of .005 seconds, the full cycle takes .01 seconds. It is a 1/.01 = 100Hz sine wave modulating the carrier. This means we have a sideband 100Hz above and 100Hz below the carrier every time the key is closed and every time the key is opened. (This assumes an identical rise and fall waveform.)

We cannot possibly have a narrower signal, or we must lengthen the rise and fall times. As a matter of fact if we ran that signal through a perfect 100Hz bandwidth filter the rise and fall times would simply change to .010 seconds at the output!!!

I've cleaned up transmitters by doing just that.

Even if I just send a single rising edge it will make a sideband above and below the carrier, and the maximum frequency distance away from the carrier would be determined by the rate of change in that rising carrier. It is nothing but AM, an amplitude modulated DSB transmission. The occupied spectrum is always the same if it is one change a second or one change an hour, because the rate and slope of change determines the ultimate bandwidth. The only thing that happens when I send faster is the sidebands appear more often.

The sidebands ALWAYS have to be out further than the keying rate because the keying rate has to always be slower than the rise and fall frequency. You can NEVER send faster than the rise and fall time alolows the carrier to turn off or on!!! That's just common sense.

Because of that, the only thing keying speed does is make it appear like sidebands are moving around inside that spectrum....but that is an illusion of time. Your receiver...just like your ears....has no memory of the leading and trailing edges. Now a storage device, either in mathematical analysis or spectral display, will show those ripples inside the primary shape....but that is because we are looking at time domain modulation of the high frequency sidebands caused by a very low frequency keying signal. It really has no effect on our receiver or our ears.

Doug Smith rewrote the ARRL Handbook's incorrect section on keying. I think Doug Smith KF6DX also has a white paper on the web that explains exactly the same thing as I just described.

The incorrect Handbook information may well have been the reason Yaesu and others put out terrible CW transmitters for many years. Either that or the engineers at those companies misused the fourier analysis and assumed the WIDEST part of the signal was determined by the CW speed. If I send 2 WPM with an unmodified FT1000D you would hear me clicking up and down about 1kHz, and if I sent 50 WPM it would be the same. The clicks would just become more frequent.

Picture a light swicth in your house. You turn it on and you hear a click in an AM radio at 1500kHz. The "carrier" frequency of the light switch is 60 Hz. The sideband is at least 1500kHz away. It's there (and everywhere in between) no matter how fast the light switch is turned off and on. But if we looked at it in a time domain that was much longer than the off and on times it would appear like there were ripples moving around inside the bandwidth, although the overall response would be exactly the same.

A drawing is worth 1000 words, and Dr. Schmidt's (W9CF) analysis shows drawings of what happens. My web page has pictures, or anyone with a storage spectrum analyzer can see the very same thing. Anyone with a receiver can hear the very same thing also.

I really wonder, since everyone can see and hear the same thing, why this same misconception keeps popping up. Especially since the ARRL has now corrected the Handbook and there are so many white papers by so many different unrelated people appearing that explain the same exact result. It is also simple basic logic. A transmitter that requires a certain bandwidth to allow the carrier to turn off and on can become wider or narrower just because we use it once a day, once a minute, once a second, or once every 50 milliseconds. It can only change if we try to turn it off and on faster than the rise and fall allows.

If a transmitter HAS to generate a sideband at least the 1/time of the complete envelope rise and fall cycle above and below the carrier to allow the carrier to move, why do some insist the bandwidth of that transition that causes all the problems suddenly is narrower if we send one dit an hour?

It occurs less frequently, but the sideband is the same bandwidth. You close the key, the signal is so wide during the rise because of the rise modulation of the envelope. You open the key, the sidebands are so wide with such an amplitude based on the fall time and shape. You send faster and it happens more often, but the shape where the trash is generated remains the same and so does the overall bandwidth of the trash.

The CW receiver that it bothers by definition CANNOT remember and store the last rise or fall and add or subtract that energy over enough keying transitions to make the ripples appear. If it did it would never be able to pass the off and on tone, and it would not be useful as a CW receiver.

The flaw in the idea that speed sets bandwidth of a transmitter is the CW keying rate is so much slower than the rise and fall time that it simply doesn't affect what we hear on a receiver. We hear the same click at the same distance regardless of speed so long as the envelope rise and fall doesn't change time or slope, we simply hear it more or less often.

73 Tom
 
RE: Bandwidth versus Keying Speed  
by W8JI on May 26, 2007 Mail this to a friend!
KE3HO,

Thank you Jim.

That's a fresh and correct contribution.

Changing the part of the waveform that is NOT producing sidebands cannot change the width of the sidebands. Very good and very simple.

There are a dozen ways to look at this, but the results are always the same.

73 Tom

 
Bandwidth versus Keying Speed  
by VE3MFN on May 26, 2007 Mail this to a friend!
Very clear and concise, and the great thing is I could read it without feeling like I was about to 'blow out a frontal lobe' on some of the math....!! Great article....

Rick VE3MFN (QRQ nut)
 
Bandwidth versus Keying Speed  
by K5MC on May 27, 2007 Mail this to a friend!
I'm sorry to see that W8JI continues to misunderstand the concept of "power" or "occupied" bandwidth. The mathematical meaning of power bandwidth is quite clear; I was also quite clear in my article that I was reporting on the 99.1% power bandwidth of the various keying waveforms that I considered.

W9CF's conclusion at http://fermi.la.asu.edu/w9cf/articles/click/index.html appears to be ". . . the keying speed does not effect (affect?) the overall bandwidth." I don't believe the term "overall" bandwidth is defined by W9CF or, for that matter, anybody else. I certainly don't recall seeing that term defined in any reputable signal analysis or communications textbook. If W9CF means the "absolute" bandwidth when he says the "overall" bandwidth, then he's clearly wrong, at least according to Fourier analysis. All signals that are limited in time have an absolute bandwidth of infinity.

Now that I've mentioned the article by W9CF, I'm afraid that while his mathematics may appear to be quite impressive, he also appears to not understand a fundamental limitation of Fourier transforms! The basic functions used in Fourier analysis are sine waves and cosine waves; these waves are precisely located in frequency but exist for all time. The frequency information of a signal calculated by the classical Fourier transform is an average over the entire time duration of the signal. (I've basically just quoted a couple of sentences from an engineering journal paper written by one of my graduate students and myself from about 10 years ago.)

If you calculate the Fourier transform of a single square-wave pulse, for example, you will clearly find that the "bandwidth" of that signal varies inversely with its time duration. (This assumes we are using a consistent definition of bandwidth, other than the absolute bandwidth. One possible definition is the 99% energy bandwidth.) I chose to use periodic keying signals in my article rather than single pulses (as assumed by W9CF) because I wanted to illustrate the concept of power bandwidth (essentially the same thing as the FCC's occupied bandwidth.) A periodic keying waveform also allows us to approach the problem via Fourier series rather than Fourier transforms. (The concept of Fourier series is simpler than that of Fourier transforms.)

I welcome anyone with a signal analysis/communications background to check my mathematics. The signal analysis that I discussed in my article (99.1% power bandwidth!) is representative of what a good junior or senior electrical engineering student is able to do after completing a typical signal analysis/communications course. I should know this because I'm an electrical engineering professor and I've taught such courses for over 20 years now.

One final note: If W8JI truly believes that the concept of occupied bandwidth is terribly wrong, then he should come up with his own precise (that is, mathematical) definition of bandwidth for the FCC engineers to consider.

73,
K5MC, Ph.D., P.E.
 
RE: Bandwidth versus Keying Speed  
by SM0AOM on May 27, 2007 Mail this to a friend!
This discussion has split into two parts.

We have the part regarding any emissions outside the "necessary bandwidth"("key clicks") caused by improper shaping of the rise and fall times of the signalling elements.

And another part that deals with the bandwidth necessary to pass the actual information.

It is perfectly acceptable to transmit radiotelegraphy
using sinusodially shaped signal elements (but the signals will be very difficult to read by ear).

In this special case we have 100% AM with a slow modulating waveform, creating a single pair of sidebands that are spaced +/- (keying rate in Baud)/2 [Hz]from the carrier or center frequency.

If the shaping is "perfect" [no discontinuites] the necessary bandwidth will be just the keying rate in Baud; no more , no less.

Convenient aural reception of telegraphy requires the
starting and ending of the signal elements to be more defined than the sinusodial shapes, and if we decrease the rise and fall times to make the elements more distinct, this will create higher order sidebands.

If an operator at the receiving end is satisfied with an element shape that results by incorporating 3 pairs of sidebands, the transmitter shaping can be set to this value and the "necessary bandwidth" becomes 3 times the keying rate in Baud.

"Key clicks" are a completely different matter.
They result from using a transmitter shaping that is not properly related to the signal element duration or keying rate.

The CCIR "necessary bandwidth" formulas have been derived assuming that the transmitter shaping is done in a proper way, and the virtues of using the Gauss Error Function as the shaping function have been known for decades in the professional world.

The spectral masks resulting from this shaping waveform have been used in i.a. type acceptance criteria for point-to-point and marine radio transmitters at least since the 60's.


73/

Karl-Arne
SM0AOM
 
RE: Bandwidth versus Keying Speed  
by W8JI on May 27, 2007 Mail this to a friend!
The problem is some people wrong assume the NECESSARY bandwidth is the ACTUAL bandwidth.

There will always be a few who cling to that mistake no matter how logic and actual measurement or operation dictates otherwise. :-)

All the theory in the world can't change what we hear with our own ears or see with our own eyes with a spectrum analyzer.

73 Tom
 
RE: Bandwidth versus Keying Speed  
by W8JI on May 27, 2007 Mail this to a friend!
http://www.doug-smith.net/cwbandwidth1.htm

Doug Smith says "Fig 2 is a spectral analysis of the waveform of Fig 1. Spectral occupancy is chiefly determined by the envelope shape and not by the keying speed. To be sure, keying such a waveform at high speed puts more energy into adjacent frequencies than at low speed; but the instantaneous amplitude of the keying sidebands is constant during the rise and fall times, regardless of keying speed."

http://fermi.la.asu.edu/w9cf/articles/click/index.html

W9CF says "This problem was brought to my attention by Tom Rauch, W8JI, who, in his note to me, had described his experience and correctly pointed out all the main features that govern the bandwith. These notes are an expanded version of my reply giving the mathematical explanation.
To fit the most CW signals into the available spectrum, we need to limit the bandwidth taken up by the signals. It is therefore useful to see how the energy in a dot or dash pulse is distributed around the carrier frequency. Here I give some notes on how to make this analysis. The main result is that the spectrum for many keying shapes is given by the product of the spectrum of a square pulse times the spectrum of the slope of the rise and fall behavior of the pulse.

It seems from my experience reading morse, that the rise time should be the main factor in producing code that can be read by ear comfortably. Since the rise time dominates the bandwidth for the usual CW signal, the analysis shows that to get a nearly optimal bandwidth to rise time, the keying pulse shape should have a gaussian slope.

In the next section I review basic Fourier analysis of amplitude modulation. I then calculate the spectrum of a pulse with an exponentially shaped rise and fall as would be produced by simple RC networks. The results suggest the more general analysis in the following section, with the conclusion that a pulse with gaussian slope, i.e. error function rise and fall shapes, will have an optimal bandwidth and rise time.

It seems likely that all of this would have been worked out by radio engineers in the early 1900s when CW signals were first employed. "

Both articles are good reading, and common sense will agree with the details in those articles.

73 Tom


 
Bandwidth versus Keying Speed  
by K5MC on May 27, 2007 Mail this to a friend!
It certainly appears to me that W8JI and some other folks on this reflector are assuming that a sinusoid (a sine wave or cosine wave) of frequency f Hz having a finite time duration has its entire spectrum concentrated at f Hz. According to Fourier analysis, at least, such an assumption is wrong! For a sinusoid of finite duration T seconds, the Fourier spectrum is spread out on either side of f Hz by the factor 1/T. In other words, the spectrum (that is, the bandwidth) of a sinusoid is inversely proportional to its time duration.

For example, let's consider two sinusoids of equal amplitude, say 1 volt. Assume that s1 is a 1-kHz sine wave that lasts for exactly 1 second and s2 is a 1-kHz sine wave that lasts for exactly 2 seconds. Therefore, s1 will consist of 1000 successive sine waves, with each wave having an amplitude and period of 1 volt and 1 millisecond, respectively. Similarly, s2 will consist of 2000 successive sine waves, with each wave also having an amplitude and period of 1 volt and 1 millisecond, respectively. The 99% energy bandwidth (just to be specific on my definition of bandwidth here) of s1 will be exactly twice as much as that of s2. By my calculations, the 99% energy bandwidth of s1 is 20.6 Hz and the 99% energy bandwidth of s2 is 10.3 Hz.

The discussion above should remind everyone that the "bandwidth" of an FM signal is not simply equal to twice the maximum deviation. For example, if the maximum deviation of a commercial FM broadcast station is limited to plus or minus 75 kHz, the bandwidth of that FM station is certainly larger than 150 kHz.

I also want to point out that spectrum analyzers are based upon the very principles of Fourier analysis that I've been discussing! Spectrum analyzers provide an approximation of the "exact" Fourier analysis that I have tried to present here. In addition to teaching the theory of signal analysis, I have some modest experience in working with "real world" signals, including such examples as the transient analysis of power engineering waveforms caused by such items as arc furnaces (which are essentially random loads during the early part of a melting cycle) and power transformers (for example, transformer inrush currents).

73, K5MC
 
RE: Bandwidth versus Keying Speed  
by W8JI on May 27, 2007 Mail this to a friend!
Mickey,

I don't know how to explain it any bettter than I and several others have already done.

1.) Bandwidth is required only when the carrier changes level. When at full power or zero power it has no bandwidth, it has no modulation.

2.) Assuming a stable carrier the rate of power level change controls the highest sideband frequency produced. The level change at that slope (or any angle of slope during the transition) controls the amplitude of the sidebands.

3.) The receiver by required function cannot store the repeating sidebands. It has to respond to the very shortest off and on period without dragging the response out or we could not hear the tones starting and stopping.

4.) When we are off frequency with a CW receiver we hear the same exact amplitude level of clicks at the same spacing no matter how fast or slow the signal is keyed. This is because the transmitter ALWAYS has to generate the same badwidth during the upward and downward transition or it simply cannot transmit the shape of the rise and fall!!!

5.) If we look at that over a long time and add the effects of the much lower frequency off and on keying, the effect is to cause ripples or peaks and valleys in the points where energy is distributed. The overall SLOPE of that sideband energy is exactly the same with one dit or a hundred dits per second, just as long as the keying rate does not approach the rise and fall rate.

6.) We cannot sort out those close spaced ripples with a receiver, so they are meaningless to the operator. We cannot sort them out because the bandwidth of the receiver has to be wider than the rise and fall frequency during the rising and falling transitions or the receiver will "mush" the transmitter by clipping sidebands. You can hear this effect as you crank in selectivity on a receiver to values below a few hundred Hz.

7.) A spectrum analyzer will store the signals and as it makes many sweeps will paint the ripples on the screen, but if we look at the envelope shape we will always find the roll off or attenuation with frequency will always match the shape required to produce the rise and fall shape of the keyed signal.

I can't say much more. All it takes is a few minutes with a receiver and a transmitter and you will see what I say above is true. The space we take up on a band with our keyclicks is entirely dependent on the shape of the rising and falling edges.

While it is true the clicks appear more frequently at higher speeds and have more average power over time at higher speeds, the overall shape of the area you bother remains exactly the same independent of keying speeds as long as those speeds are reasonable. Of course if I send one klick an hour no one would care, but if I was 1kHz away and you were sending 5-10 WPM or 50 WPM you would be placing the same energy at each off and on transition on my frequency.

Sending slower will not make this bandwidth go away.

Thinking otherwise is pobably what got Yaesu and others in big trouble. They assumed they could put out rigs with horrible ~1mS rise times.

That's why you can hear an FT1000MP clicking on CW 1kHz or more away, even when the guy is sending only 10 WPM.

I'd like to agree with you, but I can't change how the system works. I wish I could because the bands would be much cleaner and we would not need to shape the waveform of the rise and fall. All we would need to do is turn the keyer speed down.

Unfortunately CW transmitters and receivers do not behave that way, and we have to set the rise and fall times and shape carefully to avoid adjacent channel keyclicks.

It was somewhere around the 1900's we learned this, but like many core skills we have forgotten the basics.

73 Tom


 
RE: Bandwidth versus Keying Speed  
by W6TH on May 27, 2007 Mail this to a friend!
.

Very interesting discussion brother hams, but remember this, when you qso me, remember to run a pure square wave and make that keying as hard as you can as it certainly makes good copy for my head at 50 to 70 wpm.

Guess you can't teach an old dog new tricks.

73, W6TH

.:
 
RE: Bandwidth versus Keying Speed  
by AA4PB on May 27, 2007 Mail this to a friend!
Tom, how does the CW bandwidth issue compare with bandwidth of other data modes (FSK for example)? I think that is part of the confusion. We are accustomed to thinking in terms of a higher signaling rate requiring greater bandwidth and trying to apply that to CW. I don't think you are implying that 300 baud packet requires the same bandwidth as 1200 baud packet, for example.

 
RE: Bandwidth versus Keying Speed  
by VA3NR on May 27, 2007 Mail this to a friend!
I have a question on the mathematical analysis: I think the analysis assumes periodic pulse trains at the two speeds. i.e a string of dits. How does the analysis change if the transitions instead occur at random times? i.e. dashes, spaces between characters, and spaces between words are NOT integer multiples of the dot length. In fact they are not even constant - they vary throughout the transmission.

Thanks, I appreciate the presentation and discussion. Fourier study was long time ago for me and I think I purged it immediately upon graduation.

73, Chris VA3NR.
 
RE: Bandwidth versus Keying Speed  
by SM0AOM on May 27, 2007 Mail this to a friend!
For those that can read German, the ITU point of view
regarding the relation between A1A telegraphy keying rates and occupied or necessary bandwidths is elaborated on http://www.qsl.net/dk5ke/a1a.html#signal

I would be most surprised if the international
radio engineering community should have been wrong all the time on this subject.

The "key-clicks" or spurious emissions that poorly engineered equipment can generate are a separate subject.

73/

Karl-Arne
SM0AOM



 
RE: Bandwidth versus Keying Speed  
by W6TH on May 27, 2007 Mail this to a friend!
.
The "key-clicks" or spurious emissions that poorly engineered equipment can generate are a separate subject.
..............................................
This I agree.

Actually it is not poor engineering and can be overlooked. All it amounts to is time constants of a capacitor and a resistor.

On my Icom 756 Pro III, I have tried the 2, 4, 6, and the 8 ms for wave shaping and on the actual testing on the air, the operators have not by ear noticed any change. All agreed it was clean and smooth.

With my two Icom 718 radios, I have yet to have a complaint with the one exception, at high speed keying the receiving operators wanted the semi breakin keying.
This do to the shortening of dits and dahs.

...Sometimes hams get carried away...

On cw, we do not need the 3 Khz bandwidth and the use of filters can shorten the bandwidth, fiddle dee dum.

.:
 
Bandwidth versus Keying Speed  
by K5MC on May 27, 2007 Mail this to a friend!
I appreciate very much the nice comments from a number of hams regarding my article. Now I would like to respond to some comments from VA3NR and SM0AOM.

I chose a long string of dits as the keying waveform (a so-called deterministic signal) so that it would be "reasonably easy" to calculate the power bandwidth of the resulting CW signal. The keying waveform that VA3NR mentioned is a true random signal that cannot be described as a function of time and it is impossible to find its Fourier transform. The approach taken in the signal analysis world is to determine the autocorrelation function of the random signal from its statistical information; from that one can find the power spectral density (PSD) function. Finally, the power contributed by the spectral components over a specific frequency interval can be found by integrating the PSD over that frequency interval. The most difficult part in this process, as far as I'm concerned, is to determine the autocorrelation function of a random keying waveform. Although I have not pursued the professional literature on this specific topic, I would be pleasantly surprised if anybody has ever nailed down the autocorrelation function of a random Morse code keying waveform.

Assuming a long string of dits as the keying waveform pretty much assures that the "worst-case" power bandwidth is found for a given code speed and assumed rise/fall characteristics. For example, in my article I reported that the 99.1% power bandwidth of a CW transmitter using sinusoidal keying (5-ms rise/fall times) is 150 Hz at 30 wpm. The 99.1% power bandwidth of that transmitter sending a random message at 30-wpm would have to be somewhat less than 150 Hz.

Regarding SM0AOM's comments, unfortunately I cannot read German. (There's probably an English version of those ITU rules around somewhere, but I haven't looked for it.) I suspect that the ITU rules are an elaboration of what we find in Part 97, however. The FCC distinguishes between "spurious" emissions (such as harmonics), "out-of band" emissions (such as key clicks) and "necessary" bandwidth.

By the way, the so-called "necessary" bandwidth is essentially a "legal" definition in my view; it certainly isn't an engineering (that is, mathematically precise) definition compared to occupied bandwidth, power bandwidth, absolute bandwidth, null-to-null bandwidth, equivalent noise bandwidth, and several others discussed in the engineering literature. Part 2 of the FCC rules (which I referenced in my article) includes a table of necessary bandwidths for a variety of signals.

It is also interesting to note that the definition of bandwidth found in 97.3 is, in essence, the 99.75% power bandwidth. The definition actually says the following: "Bandwidth. The width of a frequency band outside of which the mean power of the transmitted signal is attenuated at least 26 dB below the mean power of the transmitted signal within the band." This is the 99.75% (that is, 0.9975) power bandwidth because

10 log (1-0.9975)/1 = 10 log 0.0025/1 = -26.02 dB

The 99.75% power bandwidth, of course, will be somewhat larger than the 99% power bandwidth (which is, in essence, the FCC's definition of occupied bandwidth) for a given signal.

In closing this round of my comments, I will once again attempt to point out to W8JI (as I did in my original article) that the concept of power bandwidth does not say that the key clicks heard from a poorly designed CW transmitter are reduced in strength if the keying speed is reduced. Some people try to read that conclusion into the concept of power bandwidth (along with the general subject of Fourier analysis!), but they are simply misreading the information provided by the power bandwidth. The power bandwidth represents the time average values of the powers contributed by the various frequency components of the CW signal. You can be sure that, regardless of what W8JI or some others might say, the "power" bandwidth (and the "occupied" bandwidth as defined by the FCC) of a CW signal does definitely vary with the keying speed as I reported in my article.

73, K5MC
 
RE: Bandwidth versus Keying Speed  
by W6TH on May 27, 2007 Mail this to a friend!
.
K5MC,

You can be sure that, regardless of what W8JI or some others might say, the "power" bandwidth (and the "occupied" bandwidth as defined by the FCC) of a CW signal does definitely vary with the keying speed as I reported in my article.
..................................................

Thanks Mickey and looking back quite a few years, I have remembered somewhat the same as above mentioned.

.......I am on your side with this one, thanks for the post and the math that finally convinced me...Don't be too shy and come visit us again.

73, W6TH
.:
 
RE: Bandwidth versus Keying Speed  
by W8JI on May 27, 2007 Mail this to a friend!
Well in closing all I can say is there are people who willtake the time to reason through the problem and understand it, or to actually perform an experiment to confirm their understanding.

In the other camp there are those who will misapply a good formula and make it apply to something it does not actually apply to.

For example our friend from Sweden says it is a transmitter "defect". But there are no transmitters I've ever seen that readjust the rise and fall times to fit the very minimum bandwidth theory dictates. I doubt anyone would want a transmitter that sounded softer and softer as speed was slowed, or that changed rise and fall times on every dot and again when a dash came along.

Indeed if we set that as the standard for a "good design", so the bandwidth actually does what a few people claim and changes with speed, then every transmitter in the world is defective.


Until the people who are misapplying the formula actually take the time to reason through the problem or get off their duffs and do a simple experiment almost any novice could do.... there will be no meeting of the minds.

73 Tom

 
RE: Bandwidth versus Keying Speed  
by W9AC on May 27, 2007 Mail this to a friend!
Mickey:

I believe you are incorrectly mixing occupied bandwidth with time.

Certainly, the amount of total time of occupied bandwidth is greater under higher WPM conditions. Why? Consider a ten-second period of keying at slow and fast WPM rates. At very slow speed, the number of rise/decay sequences may only be a fraction of rise/fall sequences at a higher WPM rate.

If I key a transmitter once during a ten-second period, there is one bandwidth-consuming rise interval and exactly one bandwidth-consuming decay interval. By contrast, perhaps 30 or more rise/decay changes occur during that same ten second period under higher WPM conditions -- but the amount of occupied bandwidth remains exactly the same in each case.

True, there may be a perception of higher occupied bandwidth with the higher WPM rate -- only because banwidth-consuming transitions are occuring more often over any given time period. However, as others have shown, the bandwidth of a pure CW signal is developed during the transition between zero and full delivered power -- and again at the transition back to zero.

The repetitions associated with keying speed have no consequence on bandwidth except perhaps as some keying extreme when keying becomes so fast that the keying rate is actually faster than the rise/decay time of the waveform; a pretty unlikely scenario.

Paul, W9AC

 
Bandwidth versus Keying Speed  
by W1YW on May 27, 2007 Mail this to a friend!
"... welcome anyone with a signal analysis/communications background to check my mathematics. The signal analysis that I discussed in my article (99.1% power bandwidth!) is representative of what a good junior or senior electrical engineering student is able to do after completing a typical signal analysis/communications course. I should know this because I'm an electrical engineering professor and I've taught such courses for over 20 years now"

-------------------------

Looks good. Thanks for contributing.

73,
Chip W1YW
(now retired from BU)
 
RE: Bandwidth versus Keying Speed  
by W9AC on May 27, 2007 Mail this to a friend!
I should clarify my previous statement in that the application of time to bandwidth is necessary but it's the way time and bandwidth are being applied in the article that yield incorrect results.

Paul, W9AC
 
Bandwidth versus Keying Speed  
by N0AH on May 27, 2007 Mail this to a friend!
I agree with the accomplished MFJ amateur radio operator..........just look at 160M. Acclaimed DXers will jump all over your attempt to DX on the topband next to their frequencies served (at table 10. 1.823MHz)You better make sure to make something perfect which cannot be made perfect. And adjusting your speed to keep within a given bandwidth is stupid. Now turning off your amplifier, (Negative QRO for you newbies), that will keep you within bandwidth more than speed. Wy no one has brought this part of the equation up is par for this course- . I still really like the article. I have it printed off and in the binder.
 
Bandwidth versus Keying Speed  
by K5MC on May 27, 2007 Mail this to a friend!
The positive feedback from both W6TH and W1YW is gratefully acknowledged.

I just realized that I was rather sloppy in my last posting, however, with my algebra in demonstrating that the bandwidth definition in Part 97.3 of the FCC rules is equivalent to the 99.75% power bandwidth. Here's a better "proof" of that statement:

10 log (Po/Pi) = -26 dB

where Po is the mean (average) power in the "outside" frequency band of the signal and Pi is the mean power in the "inside" (within the) frequency band of the signal.

Solving the equation above by dividing both sides by 10 and then taking the antilog of both sides we have

Po/Pi = 10^(-2.6) = 0.002512

Po = 0.002512 Pi

Pt = Po + Pi = 1.002512 Pi

where Pt is the total average power of the signal

Therefore, Pi = Pt/1.002512 = 0.997494 Pt. Thus, the average power of the transmitted signal within the band is very nearly 99.75% of the signal's total average power.

73, K5MC
 
RE: Bandwidth versus Keying Speed  
by AB0WR on May 27, 2007 Mail this to a friend!
For square pulses repeated at a specfic interval we can define two values.

"a" is the pulse width. T is the time measured from halfway between pulse 1 and pulse 2 to halfway between pulse 2 and pulse 3.

In essence, a/T is a measure of the duty cycle of the pulse train. If "a" is held constant and T goes up then the duty cycle gets less.

The Fourier serices coefficient "c" for such a series of pulses is defined as

(V)(a/T)[ sin(nwa/2) / (nwa/2) ]

where V is the amplitude of the pulse and w = 2pi/T

As T approaches infinity you sooner or later wind up with the inverse Fourier transform equation.

It would seem that this would mean that only your coefficient values would change, their relationship wouldn't. Thus your power bandwidth calculations would require the same number of terms giving you the same bandwidth. The power contained might not be the same.

tim ab0wr

 
RE: Bandwidth versus Keying Speed  
by SM0AOM on May 27, 2007 Mail this to a friend!
"But there are no transmitters I've ever seen that readjust the rise and fall times to fit the very minimum bandwidth theory dictates"

In fact there are such transmitters.

One that I have used myself is the Telefunken
S Steu 676 + Tg 676 exciter. It contains several rise/fall time options (realized as multi-pole low-pass filtering of the keying waveform), one of which is chosen for a given A1A keying rate. It does however not adjust its rise and fall time for the length of every signal element.

The description [1961]of this function in the transmitter quotes the CCIR Recommendation 230 from 1959, so the whole concept appears to have been well known already then by the professional and regulatory world.

Finally, I believe that the FCC 2.202 bandwidth calculations come straight out of the ITU Radio Regulations.

73/

Karl-Arne
SM0AOM
 
Bandwidth versus Keying Speed  
by W1YW on May 28, 2007 Mail this to a friend!
And adjusting your speed to keep within a given bandwidth is stupid.

----------------------

..amd yet the PHYSICS tells you the reality.

Actually, a related case comes up in SETI. It is presumed that narrow signal(s)will be transmitted at a very low bit rate, in part to keep the highest SNR: increasing bandwidth decreases the SNR for a given power.

The SNR will, in fact, decrease as your keying speed increases. Don't like that fact? Tough. And don't do moonbounce.

I am so grateful that W9AC put up a fun and informative piece, written for everyone to understand and enjoy--and refuses to be driven away just because he is smart, and worked hard to get that way.


73,
Chip W1YW
 
Bandwidth versus Keying Speed  
by W1YW on May 28, 2007 Mail this to a friend!
Apologies to K5MC--

Obviously the august article author; whereas W9AC is a cordial and worthwhile commenter.

Let's see if I get my call straight:-)

73,
Chip W1YW
 
RE: Bandwidth versus Keying Speed  
by W9OY on May 28, 2007 Mail this to a friend!
Paul writes:

"True, there may be a perception of higher occupied bandwidth with the higher WPM rate -- only because bandwidth-consuming transitions are occurring more often over any given time period. However, as others have shown, the bandwidth of a pure CW signal is developed during the transition between zero and full delivered power -- and again at the transition back to zero."

I find this statement a bit confusing. How is this perception realized? If a string of transitions are in fact causing this "perception" are you analyzing the wrong thing?

73 W9OY
 
RE: Bandwidth versus Keying Speed  
by VA3NR on May 28, 2007 Mail this to a friend!
It is the issue of time-averaging the power spectrum that’s leading to the different viewpoints. The length of time over which the power is averaged is subjective. The presentation uses a relatively large window, such that the (small) bandwidth during the constant amplitude portion pulls the average down vs. the (large) bandwidth during the transitions.

Time-averaging over long period is not useful method of looking at key clicks. Consider a transmitter sending wide clicks at 100wpm for 10 seconds but then going key-down and sending a steady carrier for 50 seconds. The calculated 1-minute time-average bandwidth would give appearance of relatively small bandwidth because most of the time the bandwidth was very narrow.

The math to prove it has long since left me, but I suspect the time average bandwidth would be directly related to the number of transitions in the time window. So for a given (long) window, and periodic keying waveform, higher speed gives larger average.

For looking at clicks, it would be more useful to use relatively small window for time averaging the spectrum. I saw FCC reg.s just mentions “mean power” and doesn’t specify time interval. There is some guidance in mean power definition in US Federal Standard 1037C:

“mean power (of a radio transmitter): The average power supplied to the antenna transmission line by a transmitter during an interval of time sufficiently long compared with the lowest frequency encountered in the modulation taken under normal operating conditions. [NTIA] [RR] (188) Note: Normally, a time of 0.1 second, during which the mean power is greatest, will be selected.”

I suspect if in the analysis, a window of only 0.1 second were used to average power, and the worst case throughout the pulse trains were selected, it would more effectively capture the clicks produced during the transitions. I suspect wpm speed would have little effect over range where there were equal number of transitions in the window.

73, Chris VA3NR

___
For those interested, definition of bandwidth for Cdn. Amateur is worded differently and doesn’t use mention average or mean power. From Industry Canada RIC-2: “The bandwidth of a signal shall be determined by measuring the frequency band occupied by that signal at a level that is 26 dB below the maximum amplitude of that signal.”
 
RE: Bandwidth versus Keying Speed  
by W9AC on May 28, 2007 Mail this to a friend!
"I find this statement a bit confusing. How is this perception realized? If a string of transitions are in fact causing this "perception" are you analyzing the wrong thing?"

Lee,

It's not that complicated. There is no "perception" being analyzed. More rise/decay transitions per unit of time will be more apparent to the listener.

Example: If someone sends a string of dits for ten seconds at 60 WPM from a transmitter generating moderate key clicks, and I listed to a weak DX station up a few hundred Hz, the interference caused by key clicks is more noticeable than locking down the key of the same transmitter for ten seconds where there is one CW rise period and one decay period. More rise/decay transitions per unit of time are more noticeable to a listener. This is the "perception" I spoke of earlier.

However, in this example, the occupied bandwidth remains the same whether the keys clicks are generated at 60WPM or 0.5 WPM.

Paul, W9AC
 
Bandwidth versus Keying Speed  
by K5MC on May 28, 2007 Mail this to a friend!
I believe AB0WR has been reviewing some of his old EE textbooks! Tim's mathematical posting is the classic analysis of a train of rectangular pulses of amplitude V and duration "a" seconds, recurring periodically every T seconds. (I used the term "square-wave" rather than "rectangular" in my article.) Because I have my latest edition of Hayt and Kemmerly (one of the most classic EE circuits books around) handy, I will simply "borrow" some observations directly from it. The bandwidth of a filter that's designed to pass these periodic pulses is a function of the pulse width but not of the pulse period. The "required" bandwidth is approximately 1/a Hz. (This turns out to be essentially the "first null" bandwidth.) Because I assumed that my keying waveform was a "string of dits" having a constant duty cycle of 50%, both a and T change proportionally with speed such that a/T = 0.5. Therefore, I found that the power bandwidth varies directly with the speed in the case of square-wave (rectangular) keying, which is exactly consistent with the theory.

SM0AOM's comment about some CW transmitters from 45 years ago having variable rise/fall characteristics is very interesting. I am not surprised to learn that that is exactly the case. There are obviously some additional issues involved regarding the rise/fall characteristics of a CW signal versus speed when a human operator is involved (for example, "harder" keying to combat QSB/QRN), but if we ignore those issues, it would be desirable to increase the rise/fall times as we decrease our sending speed. Maintaining constant rise/fall characteristics regardless of speed is certainly not the norm in modern digital communication systems. (By the way, I've looked at the keying envelope generated by my Orion II. It looks approximately sinusoidal to me. Although the software setting says 8 ms, the rise/fall times look about 5 ms according to the scope.)

As W1YW as pointed out, we can improve our S/N ratio by slowing down. QRSS is an extreme example of this fact. Indeed, the fundamental relationships between bandwidth, S/N ratio, and channel capacity as expressed by Shannon's equation are quite fascinating!

73, K5MC
 
Bandwidth versus Keying Speed  
by K5MC on May 28, 2007 Mail this to a friend!
VA3NR makes some very interesting comments. Fourier analysis can be misleading when used to study signal transients. As I pointed out earlier, the frequency information of a signal calculated by the classical Fourier transform is an average over the entire time duration of the signal. If there is a local transient over some small interval of time in the lifetime of the signal (such as the rise/fall times of a single keying pulse having a relatively long total time duration), the transient will contribute to the Fourier transform but its location on the time axis will be lost.

The "short-time" Fourier transform is one attempt to overcome this limitation, but a more recent mathematical approach to studying signal transients is "wavelet" analysis. Rather than using everlasting sinusoids, the wavelet functions are "local" both in time and frequency. There are many different families of wavelet functions, however, and choosing the most appropriate one to use for a specific signal isn't usually a trivial matter. Perhaps some day a manufacturer will develop a "wavelet" analyzer to study signal transients, but as far as I know, no such instrument is readily available and wavelet analysis remains more of a research tool. (Studying the transients generated by a variety of CW keying waveforms using wavelets would probably make an interesting research topic for my next graduate student!)

At times Fourier analysis strikes me as a very artificial way to study real signals. For example, an orchestra has a finite number of instruments, each of which that often starts and stops and starts again, with varying amplitudes and frequencies, while playing a particular piece of music over some particular time interval a < t < b. A Fourier transform can be determined for that particular piece of music. In effect, the Fourier "orchestra" consists of an infinite number of instruments (sinusoids), each one playing a very monotonous tone of constant amplitude and frequency, starting from time equal to negative infinity and continuing forever. The frequency of each instrument is infinitesimally smaller or larger than that of its adjacent instruments (continuous line spectrum). The amplitudes and phases of these sinusoids are such that they add up to the particular piece of music from a < t < b and add up to zero at all other times! Lathi [1] refers to this as the "marvelous balancing act" of Fourier transforms. It amazes me that Fourier analysis proves to be such a useful tool in the study of real signals and systems.

[1] B.P. Lathi, Modern Digital and Analog Communication Systems, 3rd ed., Oxford University Press, 1998.

73, K5MC
 
RE: Bandwidth versus Keying Speed  
by W9OY on May 28, 2007 Mail this to a friend!
Paul

My point was that analyzing a transmitted signal is not quite the same as analyzing a received signal.

Guess I was a bit too subtle

73
 
RE: Bandwidth versus Keying Speed  
by AB0WR on May 28, 2007 Mail this to a friend!
k5mc:"The "short-time" Fourier transform is one attempt to overcome this limitation, but a more recent mathematical approach to studying signal transients is "wavelet" analysis"

Are there any reasonably priced books you would recommend on this? This must be an analysis tool developed after I left school.

tim ab0wr
 
Bandwidth versus Keying Speed  
by K4GLM on May 28, 2007 Mail this to a friend!
Nice work, Mickey
I think of the phenomenon as adding and subtracting the digital signal to the carrier. This produces sums and differences, that are greater when the digital signal is greater; hence more bandwidth.
I believe Claude Elwood Shannon mathematically defined this with Shannon's theorem. (Not me, maybe a cousin or something...)
Shannon Boal K4GLM
 
Ain't seen nothing yet!  
by N4QA on May 29, 2007 Mail this to a friend!
And, if the no-coders of this world are frightened of communication via on-off keying of sinewaves, just wait 'til someone attempts to clue them in to the intricacies of the generation, modulation, transmission etc of the human voice!

CW forever!

72.
Bill, N4QA
 
Bandwidth versus Keying Speed  
by K5MC on May 29, 2007 Mail this to a friend!
In response to AB0WR's question, two books I have at home that discuss short-time Fourier transforms are:

System Analysis and Signal Processing by Philip Denbigh (Addison-Wesley, 1998, ISBN 0-201-17860-5)
Signals and Systems by Simon Haykin and Barry Van Veen (Wiley, 2005, ISBN 0-471-70789-9)

I will look in my office at school later this week for some other books. Many of the books that discuss fast Fourier transforms (FFTs) may also include a discussion of short-time Fourier transforms.

As Denbigh points out in his book, to analyze a signal whose frequency content changes with time, the waveform is divided up into segments. Each of these segments is analyzed separately by means of the FFT to give a "short-time" Fourier transform (STFT) and then the resulting spectra are displayed side by side to generate a "spectrogram." Speech is probably the most common signal used to illustrate the concepts of STFTs and spectrograms. (BTW, Denbigh's book emphasizes the use of MATLAB, one of the most popular software packages used in electrical engineering these days, at least in academic circles.)

73, K5MC
 
RE: Bandwidth versus Keying Speed  
by NI0C on May 29, 2007 Mail this to a friend!
K5MC wrote: "As W1YW as pointed out, we can improve our S/N ratio by slowing down. QRSS is an extreme example of this fact. Indeed, the fundamental relationships between bandwidth, S/N ratio, and channel capacity as expressed by Shannon's equation are quite fascinating!"

First of all, thanks for this article and discussion.

One comment I have with regard to Chip's observations on QRS is that, in order to realize the benefits of the improved s/n ratio, the person at the receiving end needs to respond by narrowing his/her receiver bandwidth.

73,
Chuck NI0C
 
RE: Bandwidth versus Keying Speed  
by W9PMZ on May 29, 2007 Mail this to a friend!
K5MC - is it possible that W8JIs conclusions are based in the rise and fall times being much greater than the keying speed, and you have the opportunity to shape the envelope (rise and fall times); and you are discussing a generalized case?

What I believe that W8JI is doing is creating a matched filter on the transmit end (e.g. controlling the rise and fall times) to fit the performance of the receiver.

After all it doesn't make much sense to have a signal rising when it needs to be falling....

73,

Carl - W9PMZ
 
Bandwidth versus Keying Speed  
by K5MC on May 29, 2007 Mail this to a friend!
As NI0C points out, the reason the SNR (signal-to-noise ratio) improves is because the receiver's bandwidth is reduced by the operator when copying very slow CW, thus reducing the average noise power. The average power of the transmitted CW signal is independent of the speed, but the "power" or "occupied" bandwidth varies with the sending speed when proportional spacing between the code characters is used. (I got somewhat "carried away" when I brought up Shannon's equation!)

Regarding W9PMZ's comments, I'm hesitant to speculate on exactly how W8JI reaches some of his conclusions. However, here's a quote from one of W8JI's posts earlier in this thread:

1. Bandwidth is required only when the carrier changes level. When at full power or zero power it has no bandwidth, it has no modulation. (W8JI)

W8JI makes this statement immediately after I had just discussed this very issue with my example of the 1-second and 2-second duration 1-kHz sine waves. As I pointed out, the 99% energy bandwidth of the 1-second duration 1-kHz sine wave is 20.6 Hz, whereas the 99% energy bandwidth of the 2-second duration 1-kHz sine wave is 10.3 Hz.

W8JI's error here is essentially that of the "pioneers" in the early days of radio broadcasting. (Lathi [1] discusses this interesting bit of history in his textbook.) Let's assume that the maximum and minimum carrier frequencies of an FM station are fc + m and fc - m, where fc and m denote the unmodulated carrier frequency and the amount of deviation, respectively. The pioneers assumed that a sinusoid of frequency f Hz has its entire spectrum concentrated at f Hz and, therefore, they reasoned that the spectrum of the FM signal would lie entirely within a bandwidth of twice that of the deviation (a value of 2m using my example), but this is incorrect because the bandwidth of a time-limited sine wave is not zero! For a sinusoid of finite duration T seconds, the spectrum (bandwidth) of the sinusoid is spread out on either side of its center frequency by 1/T Hz. The pioneers had overlooked this spreading effect as W8JI apparently continues to do.

[1] B.P. Lathi, Modern Digital and Analog Communication Systems (ISBN 0-19-511009-9)

73, K5MC
 
Bandwidth versus Keying Speed  
by W8XR on May 29, 2007 Mail this to a friend!
Mickey,

I would like to see the mathematical details underlying the bandwidth calculations, either on the
forum or off (mark.amos@toast.net)

It would be instructive to compare actual sine wave keying bandwidth in the table in addition to the 5ms rise/fall calculations that you label "Sinusoidal keying".

For instance modulating a carrier at 25 Hz (50 elements per second) you get a 60 WPM modulation.

Since a carrier modulated by a sine wave results in a copy of the modulating waveform above and below the carrier - the sidebands - I would expect a 60 WPM (25Hz) sinewave modulation to require 50 Hz of bandwidth (25 for the lower sideband plus 25 for the upper bandwidth.) I assume that your math would corroborate this "degenerate case." It would be a good way to check the numbers, in any case.

A sinewave with a period of 10 ms (5 ms "rise" and 5 ms "fall") would demand 200 Hz of bandwidth (1/.01, or 100 Hz each for the upper and lower sidebands).

I should think that _any_ modulating wave that had sinusoidal rise and falls of 5ms would require a similar bandwidth, regardless of the pulse width. At least this should be the case for normal CW keying speeds (to the point where there wasn't time for a complete modulation cycle because of rise and fall time constraints - somewhere around 200 baud - 240 WPM.) To Tom's point: while the envelope is not changing, it can't be contributing any bandwidth.

I believe it's the case that the limiting factor determining bandwidth is the envelope shape rather than the period of the modulating waveform - at least at amateur speeds.

In any case, I'm hopeful that the underlying math will help clear this up.

Mark
 
RE: Bandwidth versus Keying Speed  
by W6TH on May 29, 2007 Mail this to a friend!
.

Actually I would like to see the pulses pictured while in action, with the changing speed of from 10 wpm to 100 wpm.

As we all know:


Heaviside Step Function.......Of course, any monotonic function with constant unequal horizontal asymptotes is a Heaviside step function under appropriate scaling and possible reflection. The Fourier transform of the Heaviside step function is to be used.

The rise and fall times of the output pulses depend on the operating voltage and the time constant of R and C, but will be typically in
the order on tens of nanoseconds or to your own satisfaction. Fourier points it all out along with others, but am afraid the math is over most heads.

.:
 
Bandwidth versus Keying Speed  
by K5MC on May 29, 2007 Mail this to a friend!
W8XR: I would like to see the mathematical details underlying the bandwidth calculations, either on the forum or off (mark.amos@toast.net)

Mark, I will be glad to forward you several pages of my math details.

Regarding your keying waveform, I think you are describing a half-wave rectified sine wave. In that case, to maintain proportional spacing as I assumed earlier with my "string of dits" (50% duty cycle) keying waveform with the same rise/fall times (5 ms), the speed will be 120 wpm (50 dits per second is 120 wpm). To send at 60 wpm using a half-wave rectified sine wave, the rise/fall times will each be 10 ms. Are these the keying waveforms that you are talking about?

W8XR: To Tom's point: while the envelope is not changing, it can't be contributing any bandwidth.

Mark, to clarify my understanding, I would like to know if you think there is any difference in the "bandwidth" of the following two signals:

s1 = sin (2000 pi)t for 0 < t < 1 second and s1 = 0 for all other values of t

s2 = sin (2000 pi)t for 0 < t < 2 seconds and s2 = 0 for all other values of t

73, K5MC
 
Bandwidth versus Keying Speed  
by K5MC on May 29, 2007 Mail this to a friend!
K5MC: The average power of the transmitted CW signal is independent of the speed, but the "power" or "occupied" bandwidth varies with the sending speed when proportional spacing between the code characters is used.

My comment above concerning the average power is strictly true only if square-wave keying is assumed. For the sinusoidal keying waveform I used in my article, for example, the total average power of the 2.4-wpm signal is about 13% larger than that of the 30-wpm signal.

73, K5MC
 
RE: Bandwidth versus Keying Speed  
by W8JI on May 30, 2007 Mail this to a friend!
The overall bandwidth of the transmitter using on and off keying relates entirely to the shape and duration of the rising and falling edges. Be definition it HAS to dominate the bandwidth since the keying speed requires a small fraction of the bandwidth required by the transitions.

The only thing sending faster does is make the pulses occur more frequently. This can make the overall time-averaged LEVEL of the sidebands change, but not the overall bandwidth or slope of bandwidth.



Any formula or theorem will give an incorrect answer when people apply the formula or theorem incorrecty or incompletely by failing to understand the actual problem. The acid test is if all the numbers fit what we observe.

People tend to forget the math or a theorem is simply a tool to help us explain what we observe, and it can't really alter what we onserve. Instead of sitting here arguing endlessly and using an incomplete or misapplied analysis to prove a point that simply isn't true, it would be a better idea to spend ten minutes with a receiver or spectrum analyzer and a transmitter. If you do, you will find what I and others say is EXACTLY true.

I know some of the brightest and most experienced people in communications engineering, real engineers who take the time to understand how things actually work and who work with things like this often. Not a single person disagrees with the statement that bandwidth of a CW transmitter is entirely dependent on the rise and fall time and shape of that transition, and the only thing speed does is vary how often the sidebands occur or create peaks and nulls distributed inside that bandwidth with the same overall shape to the slope of the sidebands regardless of speed.

Either spend a few minutes with a spectrum analyzer or a real receiver and a transmitter, or live in the dark.

73 Tom







 
RE: Bandwidth versus Keying Speed  
by W8JII on May 30, 2007 Mail this to a friend!
Interesting little war we have going on here. Reminds me of the old bumblebee argument. Engineer says it's impossible for a bumblebee to fly. Wings can't provide enough lift for that big body. Can't convince the engineer otherwise. He proved it mathematically so he must be right. Right formulas----wrong application. The bumblebee flies!!!!!!!!!!!!!!

Seems to me Mr Rauch has a point get a spectrum analyzer an open your eyes and look--------------------It flies!!
73, ron
 
RE: Bandwidth versus Keying Speed  
by W6TH on May 30, 2007 Mail this to a friend!
.
It is only a squarewave generator or are all confused with the Schmitt trigger or is it the relaxation oscillator.

Then again it may be a trapazoid oscillato/generator what all are commenting about.

Possibly under load the squarewave turns into a trapazoid, uhh, just kidding.

.:
 
Bandwidth versus Keying Speed  
by K5MC on May 30, 2007 Mail this to a friend!
I continue to welcome any of W8JI's "experts" (including himself) to carefully examine the definition of power bandwidth (and occupied bandwidth) and to do the calculations themselves.

Now let me quote from page 9.7 in the 2006 edition of the ARRL Handbook:

"The bandwidth occupied by a CW signal depends on the keying rate (See the Mixers, Modulators and Demodulators chapter of this Handbook), with higher speeds requiring a wider filter to pass the sidebands. In addition, occupied bandwidth depends on the rise and fall time and the shape of the keyed RF envelope. That shape should be somewhat rounded (no abrupt transitions) in order to prevent "key clicks" - harmonics of the keying pulse. These can extend over several kHz and cause unnecessary interference. The ideal RF envelope of a code element would rise and fall in the shape of a sine wave."

The results I reported in my article are exactly consistent with what the Handbook says!

I hesitated to submit my article because I didn't want to get in a "shouting" match with W8JI and, yet, it appears that that's where we are at now. I had little hope of changing W8JI's opinion with my article, but I wanted other hams to know that the current editions of the ARRL Handbook are in agreement with the theory of Fourier analysis. I am also willing to wager a modest sum that the electrical engineers employed by the FCC will agree with my article over W8JI and his experts. As I've said many times now, the power bandwidth (and the occupied bandwidth as defined by the FCC) does vary with speed.

73, K5MC
 
RE: Bandwidth versus Keying Speed  
by KE3HO on May 30, 2007 Mail this to a friend!
I am FAR from an expert on Fourier analysis. I took ONE undergraduate course on digital signal processing where we learned about Fourier analysis, Fourier transforms, etc. The last time I used any of that was the day I took the final exam in that class, and that was 24 years ago. So if any of my comments that follow are incorrect, please feel free to tell me where I have made an error. I will state up front that I may be wrong on any one or more points, and would welcome a chance to learn.

Fourier analysis is, fundamentally, for analyzing periodic waveforms, and that it is only mathematically exact for analyzing periodic waveforms that exist from t = -infinity to t = +infinity and only then if you include all of its frequency components out to f = infinity. That is not to say that it is useless for real world analysis. It is certainly useful for analyzing real world signals. Applying it to finite duration periodic waveforms certainly yields very good results. Not exact, but very good. Good enough to be useful in the real world.

Is it not true that the extension of Fourier analysis to NON-PERIODIC finite duration waveforms involves further assumptions that might make it unsuitable for analysis of certain types of signals as well as additional approximations that make the results less accurate than applying Fourier analysis to finite duration periodic waveforms? In addition, the mathematical calculations involved in this process offer varying degrees of accuracy depending on your choice of input parameters (such as window size, window offset, number of samples, etc). Is it not true that it is an approximation that is only as good as the inputs to the algorithm, and even then it can only be “so good”. I honestly don’t know the answers to these questions, as I have never studied this method, and I am simply asking if this is true.

I think that if you wanted to synthesize the waveform of a CW signal with the keying waveform that you show in Figure 1, then the Fourier analysis would give you the necessary frequency components and amplitudes to make a VERY GOOD APPROXIMATION to the original signal. I don’t believe that the analysis will give you the spectral content of the original signal, only the spectral content of the synthesized approximation to the original signal.

K5MC said:
<< Mark, to clarify my understanding, I would like to know if you think there is any difference in the "bandwidth" of the following two signals:

s1 = sin (2000 pi)t for 0 < t < 1 second and s1 = 0 for all other values of t

s2 = sin (2000 pi)t for 0 < t < 2 seconds and s2 = 0 for all other values of t >>

I’m not Mark, but I will comment on this. K5MC will say, based on Fourier analysis, that these two signals have different bandwidths. I am not going to argue the mathematical analysis with you, as I would not know where to start the argument (and would certainly loose the argument anyway). Mathematical analysis aside, I would like to understand where the change in bandwidth comes from. I’m not talking about a mathematical explanation based on Fourier analysis because, frankly, that is the part that I don’t believe in the first place. Where does the extra bandwidth come from? When I go key down, the transmitter won’t “know” when I am going to go key up until I let go of the key. So how and where is this extra bandwidth generated? In the trailing edge of the waveform? That is the only place where the transmitter "knows" how long I am going to key down, so that must be the only place where it can suddenly generate the extra bandwidth. What is the mechanism for generating this extra bandwidth on the trailing edge?

73 - Jim
 
RE: Bandwidth versus Keying Speed  
by W6TH on May 30, 2007 Mail this to a friend!
.

... Even though the square wave generator swings the voltage output from plus to minus , the frequency does not depend upon this supply voltage. If you supplied it with a variable voltage, you could freely change the amplitude without changing the frequency. You could then make it a variable frequency source by making either C or R variable...

Good for ham use with those old xtal rigs. Less harmonics if run at 50%.

.:
 
RE: Bandwidth versus Keying Speed  
by W8XR on May 30, 2007 Mail this to a friend!
Mickie,

Thanks, I'll look forward to seeing them.

Just to clarify, the keying waveform I described is not a half wave rectified sine, but a raised sine - an actual sine wave raised by a .5 amplitude DC component. "On" is (arbitrarily) defined as anything above half the amplitude of the sine wave and "off", anything below half the amplitude.

Of course this extreme case would be "difficult" to copy, but it really is the the softest possible envelope - basically a set of Gaussian curves strung together one after the other.

Here are the details on the two examples in tabular form (much easier to see than in the narrative I used above.)

In the first example I used a 25 Hz raised sine modulating waveform:
= 25 dits and 25 dit spaces
= 50 "elements" total per second
= 1 word per second
= 60 WPM
= two 25 Hz wide sidebands
= 50 Hz total bandwidth
= 20 ms rise time and 20 ms fall time
= 40 ms wavelength

In the second example, a 100Hz raised sine as a modulation envelope:
= 100 dits and 100 dit spaces
= 200 "elements" total per second
= 4 words per second
= 240 WPM
= two 100 Hz wide sidebands
= 200 Hz total bandwidth
= 5 ms rise time and 5 ms fall time
= 10 ms wavelength

If we modulate a carrier with this 100 Hz raised sine, we'll get the carrier plus an upper side band of 100 Hz and a lower sideband of 100 Hz width, yielding 200 Hz of bandwidth.

Or, put another way: convolving a sine wave carrier with a sine wave modulation source results in the carrier +/- the modulating waveform.

Now, in my limited experience I've seen that there may be FFT resolution problems, bin bleed through, etc., (or in real radios and amplifiers there could be some non-linearity in mixing) that would fatten up the peaks and yield a wider bandwidth.

However, I contend that 200 Hz is a reasonable description of the bandwidth required for this signal - since what we're looking at is a product of mixing two sine waves.

That's what the examples were about.

I further contend that if you used a 5 ms Gaussian rise and fall time with any well behaved modulating envelope you would get the same resulting bandwidth. A DC component of a modulating signal can't modulate the carrier at all - ie. it can't have an effect on the bandwidth. (This is likely where we disagree because of the power bandwidth question, below, and the pulse width issue.)

Yes, I agree that the instantaneous power when integrated over different lengths of time would yield a power bandwidth product that is larger over longer periods of time. And, of course, what you use as the bandwidth measure affects the results (of course the -60dB bandwidth of the signal will be much wider than the -3dB bandwidth.)

Certainly a practical consequence of this could be that higher speed CW is is likely to be more annoying than lower speed CW when you're listening nearby.

However, I contend that the difference between hard and soft keying has a much greater effect on this than does the keying speed.
 
RE: Bandwidth versus Keying Speed  
by W8XR on May 30, 2007 Mail this to a friend!
Jim,

Good questions! I wished I'd asked them as well!

Mark
 
RE: Bandwidth versus Keying Speed  
by WA0LYK on May 30, 2007 Mail this to a friend!
It may be time to review the definitions in Part 2 for necessary bandwidth and occupied bandwidth.

The mathematical work being done is trying to define the minimum bandwidths required for a cw signal. A good example of this is using a sine wave rather than a square wave to analyze the needed bandwidth. By definition, this is attempting to determine the necessary bandwidth.

The folks recommending using a spectrum analyzer are by definition determining the occupied bandwidth. Trying to arrive at a mathematically correct determination for the occupied bandwidth is difficult because of all the stages and components involved.

While the statement that the "rise time" determines the bandwidth, not the keying speed, may be correct for the observed occupied bandwidth, it doesn't explain what minimum bandwidth should be.

Why is this? The difference between necessary bandwidth and occupied bandwidth in this scenario is primarily determined by the overall system performance of non-ideal circuits and is quite naturally measured by the response to a step function. It only takes one amplifier that doesn't have sufficient bandwidth, i.e. slew rate, to cause the bandwidth to increase beyond the minimum when hit with a step function.

W8JI's comments seem to infer that the rise time determines the "necessary bandwidth" and that you can see this by watching signals with a spectrum analyzer. This just isn't correct. What you are seeing with a spectrum analyzer is implementation dependent and doesn't provide information about an "ideal" signal. It is only showing the system response of a non-ideal system. The math behind what he is saying is basically defining the system response of a real world device. However, this isn't the definition of necessary bandwidth.

So why worry about it? Necessary bandwidth calculations allow a comparison between different signal types based upon a common denominator, i.e. the ideal minimum bandwidth. Occupied bandwidth's on the other hand are implementation dependent, and are useless in comparing the characteristics of given signal types.

A good example is the psk31 signal. The accepted necessary bandwidth for this is 31 Hz. Yet one only has to watch a waterfall for a short time to see that the occupied bandwidths vary all over the place because they are implementation dependent.

Jim
WA0LYK
 
RE: Bandwidth versus Keying Speed  
by W6TH on May 30, 2007 Mail this to a friend!
.
Now let me quote from page 9.7 in the 2006 edition of the ARRL Handbook:


Thanks Mickey, you are back in the game. The same is written in my 1966, The Radio Amateur's handbook. Also the wave shapes and form are shown. I will check my older books like in 1940, it may be there also.
.:
 
RE: Bandwidth versus Keying Speed  
by W6TH on May 30, 2007 Mail this to a friend!
.
According to the ARRL handbooks and to abide by the FCC rules and regulation, there seems to have been problems with keying of radio transmitters. The common cause of interference was key clicks and how to eliminate this interference.

The way was to soften the wave form and to do so was by adding a 100 ohm resistor and a capacitor of 0.1 to 0.5 Mfd, or another device called a vacuum tube keyer. The cause of key clicks was from many causes such as poor voltage regulation, sparking at the key, parasitic radiation and oscillation, etc.

By adding a capacitor and resistor to soften the keying from a square wave slowed the rise and decay time of the so called square wave. This in turn widened the bandwidth. The correction was made to perform, to match the speed of the sending operator and each transmitter had to adjust to the requirements of each individual transmitter.

In my 1940 and earlier Amateur Radio Handbook has no mention of squarewaves, that came later in years, which of course now gives us all a better understanding of key clicks, operation of speed and the proper ratio of dits and dahs.

Lets not confuse ham radio along with the commercial industry as far as band width goes, but from all evidence these squarewaves can certainly make a lot of interference on my ham radios.

.:
 
RE: Bandwidth versus Keying Speed  
by VA3NR on May 30, 2007 Mail this to a friend!
I think the answer to following question might clarify difference between infinite-time spectrum and practical spectrum measurement: Calculated by Fourier analysis, what would be the 99.1% power bandwidth of an FSK signal that continuously steps between 1 MHZ and 2 MHz in manner such that it sends a constant amplitude carrier at 1 MHZ 99.99% of the time, and the same amplitude carrier at 2 MHz remainder of the time? (I wish I could do the math - maybe I'll dig out my old textbooks too. Hopefully Mickey will help us find answer.) From looking at spectrum analyzer or listening with reciever I would say bandwidth of that signal is approximately 1 MHz, but I suspect Fourier says something different.

73, Chris.
 
RE: Bandwidth versus Keying Speed  
by W6TH on May 30, 2007 Mail this to a friend!
.
Chris, try this and is easy to understand.

http://www.dattalo.com/technical/theory/sqwave.html

.:
 
RE: Bandwidth versus Keying Speed  
by W3JJH on May 30, 2007 Mail this to a friend!
Ok, folks, here's my swing at the analysis ...

Consider a 30 word/min train of dits. It will have 1500 elements per minute or 25 per second. Half of the elements are marks and half are spaces, so we have a 12.5 Hz square wave. Harry Nyquist says that in order to reliably recover the signal, I'm gonna need a channel bandwidth at least twice that of the signal. That's 25 Hz.

Now, Morse radiotelegraphy is a double-sideband AM system, so I'll need that 25 Hz bandwidth on either side of the carrier. Thus, the minimum required bandwith for an ideal system would be 50 Hz. Practical systems (including those with a human ear as part of the decoding system) will need around two to four times the theortical minimum. Note that the "Necessary Bandwith" Table in the FCC rule [47 CFR 2.202 (g)] shows that 25 word/min requires 100 Hz of bandwidth for fading circuits. That would imply around 120 Hz for 30 word/min.

Of course, the occupied bandwidth of the transmitted signal will be much wider than the required receiver bandwidth. A 30 word/min dit train with hard rise times modulating a carrier will result in a occupied bandwidth of around 525 Hz (taking the FCC's 99.5 percent of radiated power definition). This is because the modulating waveform is rich in harmonics which will appear in the upper and lower sidebands.

Rolling off those harmonics by slowing down the rise and fall times will reduce the occupied bandwidth. This technique can allow a 30 word/min signal to fit in 200 Hz of bandwidth. The same rise and fall times will permit a 12 word/min signal to pass with essentially all of its switching harmonics intact. They will also allow for useable transmission of a 50 word/min signal.
 
Bandwidth versus Keying Speed  
by K5MC on May 30, 2007 Mail this to a friend!
KE3HO: Is it not true that the extension of Fourier analysis to NON-PERIODIC finite duration waveforms involves further assumptions that might make it unsuitable for analysis of certain types of signals as well as additional approximations that make the results less accurate than applying Fourier analysis to finite duration periodic waveforms?

Jim, I think you are confusing Fourier series and Fourier transforms. Fourier analysis is a rather broad term that includes such tools as Fourier series, Fourier transforms, FFTs, STFTs, etc. Strictly speaking, we have to assume that a signal is periodic (that is, it repeats itself over and over again from time equal to negative infinity to time equal to positive infinity) to use the technique of Fourier series. A Fourier transform can be found for both periodic and non-periodic signals, but it is particularly useful when we are dealing with non-periodic signals such as a finite-duration pulse. The inverse relationship between a pulse's time duration and magnitude spectrum (bandwidth) illustrated by the Fourier transform is among the most fundamental aspects of Fourier analysis.

KE3HO: I’m not Mark, but I will comment on this. K5MC will say, based on Fourier analysis, that these two signals have different bandwidths. I am not going to argue the mathematical analysis with you, as I would not know where to start the argument (and would certainly loose the argument anyway). Mathematical analysis aside, I would like to understand where the change in bandwidth comes from. I’m not talking about a mathematical explanation based on Fourier analysis because, frankly, that is the part that I don’t believe in the first place. Where does the extra bandwidth come from? When I go key down, the transmitter won’t “know” when I am going to go key up until I let go of the key. So how and where is this extra bandwidth generated? In the trailing edge of the waveform? That is the only place where the transmitter "knows" how long I am going to key down, so that must be the only place where it can suddenly generate the extra bandwidth. What is the mechanism for generating this extra bandwidth on the trailing edge?

Jim's comments above are very interesting and I have also thought along these lines before. As I've tried to point out, Fourier analysis is an approximation to the real world; I'm amazed that it works as well as it does in modeling real signals and systems.

To be perfectly honest, I really don't know where the extra bandwidth comes from, but human logic would very likely say that the "bandwidth" is "generated" at the trailing edge for the reason you point out. If I ignore Fourier analysis and simply look at s1 and s2, I would probably believe that both signals have the same "bandwidth" because, in part, I wouldn't have a mathematically precise definition of bandwidth to start with! For that matter, shouldn't the "bandwidth" be zero Hz because s1 and s2 are sine waves that begin and end smoothly?

If we smoothly sweep the carrier frequency plus and minus 75 kHz about the center frequency using, for example, a 1-kHz sine wave as the modulating signal, shouldn't the spectrum of this FM signal lie entirely within a bandwidth of 150 kHz? After all, according to W8JI, the carrier amplitude isn't changing.

At the end of the day, I have to trust some mathematics to quantify such concepts as energy signals, power signals, harmonics, average power, and bandwidth. Unlike most concepts in signal analysis, there are many different definitions of "bandwidth" and that fact is what prompted me to post my article in the first place. I wanted some hams to understand that if one calculates the "power" bandwidth (which has a precise definition), then one definitely finds that the keying speed is a factor in determining that specific bandwidth.

By the way, if W8JI and W9CF mean "absolute" bandwidth when they use the terms "overall" and "actual" bandwidth, then I'm in perfect agreement with them. (The absolute bandwidth is defined to be f2 - f1, where the spectrum is zero outside the interval f1 < f < f2 along the positive frequency axis.) The absolute bandwidth of any finite-duration signal is equal to infinity and the sending speed is not a factor. All man-made signals, strictly speaking, are energy signals and have an infinite bandwidth according to Fourier analysis.

I also noticed that KF6DX (http://www.doug-smith.net/cwbandwidth1.htm) "hedges his bet" by writing that "Spectral occupancy is chiefly determined by the envelope shape and not by the keying speed." "Chiefly determined" doesn't exactly sound like "wholly determined" to me!

73, K5MC
 
Bandwidth versus Keying Speed  
by K5MC on May 30, 2007 Mail this to a friend!
W8XR: Here are the details on the two examples in tabular form (much easier to see than in the narrative I used above.)

OK, Mark, I think I'm clued in now on your keying waveforms. You are actually talking about classic single-tone amplitude modulation (tone frequencies of either 25 Hz or 100 Hz), or DSB-AM. (Your modulation index happens to be 100%.) Therefore, ignoring all the imperfections in the hardware (which is what I did in my article), I agree that the bandwidth will be either 50 Hz or 200 Hz as you said. (These bandwidths would even be the so-called "absolute" bandwidths because, in practice, we are assuming these signals to be sufficiently long in duration so that the spectra of the sinusoids are essentially impulse functions.) As you also pointed out, I believe these signals would be rather difficult for a human operator to copy!

W8XR: Certainly a practical consequence of this could be that higher speed CW is is likely to be more annoying than lower speed CW when you're listening nearby. However, I contend that the difference between hard and soft keying has a much greater effect on this than does the keying speed.

Mark, I hope nobody thought I ever contended otherwise. I believe practically all of us agree that it is important to properly shape the keying waveform to avoid key clicks. I was also very careful to point out that the concept of occupied bandwidth does NOT say that the strength of the key clicks generated by a poorly designed transmitter is reduced when the sending speed is decreased. The focus of my article was simply to demonstrate the fact that the "power" bandwidth (or the "occupied" bandwidth as defined by the FCC) is a function of both the keying speed and the keying waveform. For the umpteenth time I welcome anyone having a good grasp of the theoretical/mathematical concepts involved (power bandwidth, average power, Fourier analysis, etc.) to either do the calculations themselves or to check mine.

73, K5MC
 
RE: Bandwidth versus Keying Speed  
by W8JI on May 30, 2007 Mail this to a friend!
Hi Jim,

I am VERY clear in saying the rise and fall times set the actual sideband (keyclick) bandwidth of the transmitter, and that bandwidth that causes all the problems has NOTHING to do with the CW speed. The CW speed only determines how often the sidebands necessary to modulate the carrier repeats, so speed can contriool power over time, but the receiver by definition cannot have a memory of that time through the signal processing channel.

If the receiver did have energy storage over the time of Morse characters it could not produce the off and on tones. They would neither start or stop. They would blend.

This simply has to be true because the shape and level changes in the rising and falling edges require a certain spectrum, and that spectrum by definition is always much higher than the frequency of the off and on keying.

Some people will beat this to death in order to misuse or misapply a good formula, and never lift a finger to observe what they are attempting to define.

Others of a more curious mindset will send a series of dots with a transmitter and observe the results on a receiver or spectrum analyzer and see that I and many others who have thought this problem through (and the new Handbook where the errors were corrected) are correct.

W8XR is a person who went through this on his own and reached his own conclusions. You can read what people who actually thought this problem through or did experiments at the following links:

http://www.sm5bsz.com/others/occbw.htm

Doug was instrumental in developing the Ten Tec Orion CW transmitting system.

http://fermi.la.asu.edu/w9cf/articles/click/index.html

You can read about Kevin's work at this link:
http://physics2.asu.edu/people/atkes

and the list can go on and on.....



The fact is we cannot have the shape and duration of the rise and fall times without the signal occupying a bandwidth that allows that shape, and that is true no matter how fast or slow we send.

When claims or analysis do not fit actual results the best course is to correct the analysis, since the results already prove the flawed analysis without room for any argument.

Those who are truly curious will actually take the time to observe the real life actions of the transmitter, not what they imagine happens.

73 Tom



 
RE: Bandwidth versus Keying Speed  
by W8XR on May 30, 2007 Mail this to a friend!
Thanks for providing the details of your calculations. I'm in the midst of some practical DSP work and hope to be able to make some sense of the discrepancy between the "intuitive" analysis that I've used and the mathematic analysis that you've performed.

The piece that really bothers me is that leading edge / trailing edge bit. I just can't fathom how bandwidth could possibly depend on the distance between them. Also, except for extreme speeds, the bandwidth required for even reasonable shapes should swamp any bandwidth required because of the keying speed.

However, I believe that the math SHOULD agree with experience. So, I come to one of several conclusions: there's something wrong with the application of the Fourier transform to this problem, or there's some piece of knowledge I'm missing that would invalidate the intuitive approach. If there is some problem with the application of the math, I think it will be very useful to understand why this is the case.

In any case, often, when there is controversy there is knowledge to be got - and I intend to get it.

This particular problem (the problem of the discrepancy between the math and experience) is just too interesting to let it go.
 
RE: Bandwidth versus Keying Speed  
by W8JI on May 30, 2007 Mail this to a friend!
I think the problem here is Mickey is considering a transmitter that readjusts the rise and fall to match the CW speed.

If I'm not mistaken Mickey assumes the transmitter somehow adjusts the rise and fall times to the minimum reqired to allow a CW signal of a certain speed assuming a raised sinewave. This would be a wave that starts at the negative peak as a zero, and increases to the positive peak where it rolls over and flattens off during the on tie. A shape just like a sinewave except it starts at zero and goes up through maximum where it then turns downward to zero.

The problem is, and where we disagree is, I consider the CW genrated by a NORMAL transmitter of excellent design to have a fixed rise and fall duration. This the way every single CW transmitter that has every been built works. I'm looking at a real system.

I consider a POOR design to be a transmitter that has a shape like the ARRL Handbooks used to describe, like a CW signal generated through a R C filter, or one with otherwise good shaping that has needlessly fast rise and/or fall times.

This is probably the only difference between what Mickey is saying and what I (and others) say.

This is why in the very beginning I said Mickey is looking at the minimum bandwidth required and not the actual bandwidth used by transmitters.

Unless the transmitter somehow readjusts the envelope rise and fall to match the speed and the CW is sent with the softest possible rise and fall of perfect shape at every speed you can toss the formulas out the window.

It's important to note these differences between the REAL world and what humans accept as a good sounding signal than can make it through noise or fading conditions and a theoretical system that does not apply to communication systems and that everyone would find unusable.

73 Tom




 
RE: Bandwidth versus Keying Speed  
by W3JJH on May 30, 2007 Mail this to a friend!
W8JI:

Tom, with a DSP-based radio it is not impossible to control the rise and fall time of the keying based on the the keyer dit speed. It's not even particularly hard with some analog radios. The necessary low-pass filtering can be made to track the keyer dit speed quite easily in a low-level system. I've designed such circuits for use in pulse-rate-modulation telemetry systems. Of course, linear amplification is required following the modulation, so high-efficiency power amps can't be used, but the finals in all my store-bought HF radios are class-AB these days.

73 de W3JJH
John
 
Bandwidth versus Keying Speed  
by K5MC on May 30, 2007 Mail this to a friend!
W8JI: I think the problem here is Mickey is considering a transmitter that readjusts the rise and fall to match the CW speed.

No, I am not considering such a transmitter in my article!

W8JI: If I'm not mistaken Mickey assumes the transmitter somehow adjusts the rise and fall times to the minimum reqired to allow a CW signal of a certain speed assuming a raised sinewave.

No, I am not assuming any such thing!

W8JI: The problem is, and where we disagree is, I consider the CW genrated by a NORMAL transmitter of excellent design to have a fixed rise and fall duration. This the way every single CW transmitter that has every been built works. I'm looking at a real system.

I think we disagree on some things, but this particular item is not one of them!

K5MC: Since we want to maintain the same rise/fall characteristics (shapes and times) regardless of speed, we will only vary the time duration of the constant amplitude portion of each pulse (designated as tc) to increase or decrease the number of dits sent per second. (This is a direct quote from my article.)

Tom, I thought I went to great pains in my article to explain that my 5-ms sinusoidal keying waveform had a constant 5-ms rise time and a constant 5-ms fall time at both 2.4 wpm and 30 wpm. The only thing that changed in my sinusoidal keying waveform when the speed was changed from 2.4 wpm to 30 wpm was the "center" time of the pulses (dits) when the keying pulse amplitude was fixed at a constant value of 1. Please read my article again and look at the keying waveform as it is drawn. Again, the only thing that changes in my sinusoidal keying waveform when the speed of the string of dits is changed from 2.4 wpm to 30 wpm is the time duration denoted by "tc" in the waveform sketch. As you say above, this is how normal CW transmitters work and that is EXACTLY what I assumed!

For my second keying waveform, I assumed the rise and fall times of the keying waveform were zero and referred to it as "square-wave" keying.

73, K5MC
 
RE: Bandwidth versus Keying Speed  
by KE3HO on May 30, 2007 Mail this to a friend!
W8XR: << The piece that really bothers me is that leading edge / trailing edge bit. I just can't fathom how bandwidth could possibly depend on the distance between them. Also, except for extreme speeds, the bandwidth required for even reasonable shapes should swamp any bandwidth required because of the keying speed. >>

This is where I have problems too. There is a huge disconnect between the theory presented and the physical processes involved (IMHO). The rise time and fall time and their shape are fixed and independent of keying speed . Those waveforms should produce sidebands and the spectral content of those sidebands should be independent of keying speed. During tc, the carrier is constant and unmodulated. Mickey is saying that the duration of tc affects the bandwidth of the transmitted signal. I have a big problem with this. What is the physical process by which this happens? During tc, you have an RF oscillator running at a fixed frequency and amplitude. Each cycle of the sine wave looks just like the one before it and just like the one after it. So what is the connection between duration and bandwidth? I just don't see it. If the duration of tc affects bandwidth, how is that physically produced? Once I go key down and get through the rise time to the start of the tc period, the length of tc is set by how long I hold the key down. But during tc, the RF oscillator and PA can't predict when I am going to go key up, so how can the bandwidth of the signal change? As I said earlier, the end of tc is defined by when I go key up which is the start of the fall time. The only way there could be some physical mechanism for the duration of tc to affect the bandwidth would be if somehow the duration of tc was somehow "remembered" by the rig and all of the "extra bandwidth" was created during the fall time. When I said this earlier, I was not seriously suggesting that this might be the case. Rather, I was trying to show this to be a paradox. I'm with you Mark, I just don't see the physical means to produce this extra bandwidth.

This has been a truly interesting thread, and I have read everything that everyone has said. I agree with Tom that the "obvious" thing to do is to take a spectrum analyzer and see what really happens with a real rig in the real world. I wish I had the equipment to do that.

Let me put forward one last idea for consideration. Mickey talks about the power bandwidth, and I wonder if that is somehow the source of our disagreement. Here is what I am getting at. It is my belief that, for a fixed rising and falling keying waveform, that the sidebands produced during the rise time and fall time are completely determined by the shape of the rising and falling keying waveform, and that these sidebands are independent of keying speed. I also believe that during tc, no sidebands are produced and that the bandwidth of the signal during tc is determined by the stability (in frequency and amplitude) of the transmitter. As keying speed changes, the only thing that changes in Figure 1 is the duration of tc. During the rise and fall times, you have an AM signal - the carrier modulated by the rising and falling keying waveforms. During these periods, you have 2/3 of your power in the carrier, and 1/3 divided between the two sidebands (I hope I remember the distribution of power correctly). During tc, 100% of the power is in the carrier alone. If you key faster, tc becomes shorter. When this happens, the amount of power in the sidebands during the rise and fall is the same, but the amount of power in the carrier during tc is less. The fixed amount of power in the sidebands becomes a larger fraction of your total power integrated over the entire transmitted pulse width. If the "power bandwidth" is determined by calculating the spectral width which contains 99.1% of your total integrated power, then I can see a connection between the keying speed and this "power bandwidth". If you key very slowly and tc is 1 second, then the power contained in the sidebands (generated during the rise time and fall time) is an insignificant part of your total integrated power. If you key so fast that tc goes to zero, then a full 1/3 of your total integrated power will be in these same sidebands. However, the spectral width of and the total power contained in these sidebands will nevertheless be the same at any keying speed.

I truly appreciate all of the effort that everyone has put into their contributions on this thread. This has been one of the most interesting threads here in a long time, and I will add that, IMO, the tone of the thread has been pretty pleasant also - it has not degraded into a playground fight like some of the threads have in the past. This has been a pleasure. Thank you everyone.

73 - Jim
 
Bandwidth versus Keying Speed  
by AB7E on May 31, 2007 Mail this to a friend!

I think KE3HO is correct in his explanation of the differences in perspective here. It makes sense ... clearly rise and fall times are the only transition that take up spectrum, but making them happen more often would increase the time density ("power bandwidth"?) of that use of bandwidth. In practical terms we only hear that which the rise and fall times cause, but the keying speed affects the time-averaged percentage of where the power ends up spectrally.

I have a son (not a ham) who has an advanced math degree and works as a software development engineer with a company doing signal processing work for the government. I asked him to check this thread and he came to the same conclusion.

What I don't understand is how a university math professor can't figure out how to rationalize the math to match real life. How did this thread not converge days ago?

 
Bandwidth versus Keying Speed  
by K5MC on May 31, 2007 Mail this to a friend!
W8XR: The piece that really bothers me is that leading edge / trailing edge bit. I just can't fathom how bandwidth could possibly depend on the distance between them.

Mark, the following four sentences are found on page 89 in Lathi's textbook [1]:

"Reciprocity of Signal Duration and Its Bandwidth - The scaling property implies that if g(t) is wider, its spectrum is narrower, and vice versa. Doubling the signal duration halves its bandwidth, and vice versa. This suggests that the bandwidth of a signal is inversely proportional to the signal duration or width (in seconds). We have already verified this fact for the gate (rectangular) pulse, where we found that the bandwidth of a gate pulse of width T seconds is 1/T Hz."

Most textbooks that discuss Fourier transforms will also discuss the various Fourier transform operations/properties, such as scaling, time shift, frequency shift, time convolution, and frequency convolution. I'm pretty sure that Fourier transforms, along with the various transform operations, are used by many practicing engineers as they go about designing and analyzing "real world" communication systems. I know for a fact that these topics are included in the typical undergraduate signal analysis/communication courses in electrical engineering.

By the way, when Lathi says that the "bandwidth" of a gate pulse of width T seconds is 1/T Hz, he is referring to the "first-null" bandwidth. However, his general statement regarding the inverse relationship between time duration and "bandwidth" is equally valid for almost every other type of bandwidth found in the literature, such as the 99% energy bandwidth (for energy signals) and the 99% power bandwidth (for power signals). The only type of "bandwidth" precisely defined in the professional literature in which Lathi's statement does not hold, as far as I know, is the absolute bandwidth. However, the absolute bandwidth is of little practical value when comparing real signals.

In closing here, I would like to remind everyone that if you want to increase the information rate (more information transmitted per unit of time) without increasing the signal power, the "bandwidth" must increase as well. (Let me hasten to say that the exchange of bandwidth and signal power is not possible in AM systems as it is in digital and FM/PM systems.) Mother Nature does not allow us a "free lunch" in this regard. This simple fact is another reason why nobody should be surprised that the "power" bandwidth of a CW signal varies with the keying speed as my article demonstrated. (Yes, even for keying waveforms that have identical rise/fall shapes and times!)

[1] B.P. Lathi, Modern Digital and Analog Communication Systems (ISBN 0-19-511009-9)

73, K5MC
 
Bandwidth versus Keying Speed  
by K5MC on May 31, 2007 Mail this to a friend!
KE3HO: Those waveforms should produce sidebands and the spectral content of those sidebands should be independent of keying speed.

Jim, don't forget that the location of these sidebands along the frequency axis varies with speed. When sending the string of dits at 2.4 wpm, the fundamental frequency f1 of the keying waveform is exactly 1 Hz because the time period T between consecutive dits at this speed is exactly 1 second (T = 1/f1). However, when sending the string of dits at 30 wpm, the fundamental frequency of the keying waveform is exactly 12.5 Hz because the period between consecutive dits at this speed is exactly 80 ms.

KE3HO: If you key faster, tc becomes shorter. When this happens, the amount of power in the sidebands during the rise and fall is the same, but the amount of power in the carrier during tc is less.

Below are the first several Fourier coefficients for the sinusoidal keying waveforms I studied in my article. (I calculated these coefficients out to 7 decimal places to minimize round-off errors.)

For the 2.4-wpm keying waveform with 5-ms sinusoidal rise/fall times:

a0 = 0.4963662 V (dc or average value of keying waveform)
a1 = 0.6365602 V (fundamental frequency coefficient at 1 Hz)
a2 = 0.0072660 V (second harmonic coefficient at 2 Hz)
a3 = -0.2120282 V (third harmonic coefficient at 3 Hz)
etc.

For the 30-wpm keying waveform signal with 5-ms sinusoidal rise/fall times:

a0 = 0.4545775 V (dc or average value of keying waveform)
a1 = 0.6273706 V (fundamental frequency coefficient at 12.5 Hz)
a2 = 0.0878988 V (second harmonic coefficient at 25 Hz)
a3 = -0.1856182 V (third harmonic coefficient at 37.5 Hz)
etc.

The value of a0 is "responsible" for the amount of power in the carrier. Therefore, for the sinusoidal keying waveform, the amount of power in the carrier is less for the faster speed. However, the amount of power contained by the respective sidebands is also different for the two speeds. For example, the power of the first pair of sidebands in the 2.4-wpm CW signal is larger than that in the 30-wpm CW signal because the value of a1 for the slower keying waveform is larger than that of the faster keying waveform.

To calculate the average power of each frequency component, let's assume R = 1 ohm for convenience.

For the 2.4-wpm sinusoidal keying waveform we have the following average powers per frequency component:

At 0 Hz (DC) we have (0.4963662)2 = 0.2463794 W
At 1 Hz (fundamental) we have (0.6365602/1.414)2 = 0.2026045 W
At 2 Hz (second harmonic) we have (0.0072660/1.414)2 = 0.0000264 W
At 3 Hz (third harmonic) we have (-0.2120282/1.414)2 = 0.022478 W
etc.

(Remember to divide the amplitudes by the square root of 2 (shown above as 1.414) to obtain the rms values of the various cosine terms and then square the rms values to get the average powers on a 1-ohm basis.)

For the 30-wpm sinusoidal keying waveform we have the following average powers per frequency component:

At 0 Hz (DC) we have (0.4545775)2 = 0.2066407 W
At 12.5 Hz (fundamental) we have (0.6273706 /1.414)2 = 0.1967969 W
At 25 Hz (second harmonic) we have (0.0878988 /1.414)2 = 0.0038631W
At 37.5 Hz (third harmonic) we have (-0.1856182 /1.414)2 = 0.0172271W
etc.

The total average powers of the sinusoidal keying waveforms are as follows:

Pavg = 0.49500 W for 2.4-wpm keying signal at 5-ms sinusoidal rise/fall times

Pavg = 0.43750 W for 30-wpm keying signal at 5-ms sinusoidal rise/fall times

When you add up the average powers of the DC component and the first 17 harmonic components for the 2.4-wpm keying signal, you get 0.4906272 W, which is 99.12% of the total average power (0.49500 W). Therefore, the 99.12% bandwidth of the 2.4-wpm keying signal (5-ms rise/fall times) is 17 Hz. When you use this waveform to key a CW transmitter, the resulting 99.12% bandwidth of the output signal will be exactly twice as much, 34 Hz. (I rounded 99.12% to 99.1% in my article.)

When you add up the average powers of the DC component and the first 6 harmonic components for the 30-wpm keying signal, you get 0.4337106 W, which is 99.13% of the total average power (0.437500 W). Therefore, the 99.13% bandwidth of the 30-wpm keying signal (5-ms rise/fall times) is 75 Hz, since 6 X 12.5 Hz = 75 Hz. When you use this waveform to key a CW transmitter, the resulting 99.13% bandwidth of the output signal will be exactly twice as much, 150 Hz. (I rounded 99.13% to 99.1% in my article.)

The approach is the same for square-wave keying, but this is a "standard" waveform that is readily found in the textbooks. The Fourier series for the 2.4-wpm and 30-wpm periodic signals assuming square waves (50% duty cycle as before) are given by s1(t) and s2(t), respectively, as follows:

s1(t) = 0.5 + (2/pi)[cos(2 pi t) - 1/3 cos(6 pi t) + 1/5 cos(10 pi t) - . . . ]

s2(t) = 0.5 + (2/pi)[cos(25 pi t) - 1/3 cos(75 pi t) + 1/5 cos(125 pi t) - . . . ]

(I would like to point out here that the Fourier series for the 5-ms sinusoidal keying waveforms have both even and odd harmonic frequency components, but the square-wave keying waveforms only contain odd harmonics because the square-wave keying waveforms have so-called half-wave symmetry.)

The total average power of s1(t) is exactly the same as that of s2(t), 0.5000 W. If we add the average powers of the frequency components up through the 21st harmonic for the 2.4-wpm signal, we will have 0.495398 W, which is 99.08% of the total. (I rounded this up to 99.1% in my article.) Therefore, the 99.1% power bandwidth of the 2.4-wpm square-wave keying signal is 21 Hz; thus, the 99.1% power bandwidth of the CW signal will be 42 Hz.

Likewise, we need the frequency components up through the 21st harmonic for the 30-wpm signal to have 99.08% of the total. Therefore, the 99.1% power bandwidth of the 30-wpm square-wave keying signal is 21 X 12.5 Hz = 262.5 Hz; thus, the 99.1% power bandwidth of the CW signal will be 525 Hz.

KE3HO: However, the spectral width of and the total power contained in these sidebands will nevertheless be the same at any keying speed.

For the CW signal with square-wave keying, the distribution of the average powers is identical for the two speeds. However, since the fundamental frequency of the 30-wpm keying waveform is 12.5 times higher than that of the 2.4-wpm waveform, the 99.1% power bandwidth is likewise in that exact same ratio for the two speeds. However, as shown above, the distribution of the average powers is not identical for the sinusoidal keying waveforms because those two waveforms are not equal to each other by a simple scaling factor like the square-wave keying waveforms are.

KE3HO: If the "power bandwidth" is determined by calculating the spectral width which contains 99.1% of your total integrated power, then I can see a connection between the keying speed and this "power bandwidth". If you key very slowly and tc is 1 second, then the power contained in the sidebands (generated during the rise time and fall time) is an insignificant part of your total integrated power.

Jim, as you can see from my details above, you are getting extremely warm! I am very happy that you have "hung in" here on this somewhat esoteric topic/thread.

73, K5MC
 
Bandwidth versus Keying Speed  
by K5MC on May 31, 2007 Mail this to a friend!
AB7E: I have a son (not a ham) who has an advanced math degree and works as a software development engineer with a company doing signal processing work for the government. I asked him to check this thread and he came to the same conclusion.

If your son doesn't have a background in signal analysis equivalent to that typically included in an undergraduate electrical engineering curriculum, then I'm not too surprised that he doesn't understand the concept of power bandwidth and the results I discussed in my article. If he does have such a background, then it appears that he needs to review the definition of power bandwidth, along with the other basic principles of Fourier analysis as applied to signals and systems. (If all of his degrees are in math, then I'm pretty sure that he doesn't have the background of which I speak.)

AB7E: What I don't understand is how a university math professor can't figure out how to rationalize the math to match real life. How did this thread not converge days ago?

If you want to take me to task for continuing to try to open the eyes of some hams, I think you should at least understand that I am an electrical engineering professor, not a math professor!

73, K5MC
 
Bandwidth versus Keying Speed  
by K5MC on May 31, 2007 Mail this to a friend!
K5MC: At 0 Hz (DC) we have (0.4963662)2 = 0.2463794 W
At 1 Hz (fundamental) we have (0.6365602/1.414)2 = 0.2026045 W
At 2 Hz (second harmonic) we have (0.0072660/1.414)2 = 0.0000264 W
At 3 Hz (third harmonic) we have (-0.2120282/1.414)2 = 0.022478 W
etc.

I just noticed that the formatting screwed up when I posted my Word file to the eham site. The equations above involving the squared terms should look like this:

At 0 Hz (DC) we have (0.4963662)^2 = 0.2463794 W
At 1 Hz (fundamental) we have (0.6365602/1.414)^2 = 0.2026045 W
At 2 Hz (second harmonic) we have (0.0072660/1.414)^2 = 0.0000264 W
At 3 Hz (third harmonic) we have (-0.2120282/1.414)^2 = 0.022478 W
etc.

K5MC: At 0 Hz (DC) we have (0.4545775)2 = 0.2066407 W
At 12.5 Hz (fundamental) we have (0.6273706 /1.414)2 = 0.1967969 W
At 25 Hz (second harmonic) we have (0.0878988 /1.414)2 = 0.0038631W
At 37.5 Hz (third harmonic) we have (-0.1856182 /1.414)2 = 0.0172271W
etc.

Likewise, these intended equations are as follows:

At 0 Hz (DC) we have (0.4545775)^2 = 0.2066407 W
At 12.5 Hz (fundamental) we have (0.6273706 /1.414)^2 = 0.1967969 W
At 25 Hz (second harmonic) we have (0.0878988 /1.414)^2 = 0.0038631W
At 37.5 Hz (third harmonic) we have (-0.1856182 /1.414)^2 = 0.0172271W
etc.

The ability to post math equations on eham is rather limited!

73, K5MC
 
Bandwidth versus Keying Speed  
by K5MC on May 31, 2007 Mail this to a friend!
K5MC: If you want to take me to task for continuing to try to open the eyes of some hams, I think you should at least understand that I am an electrical engineering professor, not a math professor!

I want to apologize to AB7E for all of my comments directed to him. After reading his post again, I believe that I misinterpreted much, if not all, of what he was saying. I will try very hard to avoid doing that again!

73, K5MC
 
RE: Bandwidth versus Keying Speed  
by W8JI on May 31, 2007 Mail this to a friend!
I have limited time to follow this thread, but rereading some parts it looks like Mickey is using a long time period average power that includes many off and on cycles to determine bandwidth.

Everyone agrees or should agree as fixed shape and level pulses occur more and more frequently there are more of them in a given time period, twice as many at twice the speed. He then compares that long term accumulation of sidebands to the power in the transmitter.

This long term accumulation of enery in clicks is NOT what causes the problem on adjacent channels when we are operating CW. By definition neither our brains nor or receivers can accumulate or store that energy.

Our only perception is the clicks occur more often. As we look at them on the receiver they cause more frequent QRM but not stronger QRM, within limits or reasonable CW speeds.

The off and on transitions ALWAYS occupy the same overall bandwidth because they are caused by rise and fall periods, not the spaces between the rise and fall times.

The spaces between the rise and fall times cannot affect the bandwidth occupied by the rises and falls. The rises and falls are so brief they set the ultimate space occupied by the CW signal, not the much slower Morse rate.

I think the difference of opinion would go away if people considered how the system actually works.

You cando this by sending dots and tuning across the signal with a real receiver.

73 Tom
 
RE: Bandwidth versus Keying Speed  
by WA0LYK on May 31, 2007 Mail this to a friend!
KE3HO
>>W8XR: << The piece that really bothers me is that
>>leading edge / trailing edge bit. I just can't fathom
>>how bandwidth could possibly depend on the distance
>>between them. Also, except for extreme speeds, the
>>bandwidth required for even reasonable shapes should
>>swamp any bandwidth required because of the keying
>>speed. >>

>>This is where I have problems too. There is a huge
>>disconnect between the theory presented and the
>>physical processes involved (IMHO). The rise time and
>>fall time and their shape are fixed and independent
>>of keying speed . Those waveforms should produce
>>sidebands and the spectral content of those sidebands
>>should be independent of keying speed. During tc, the
>>carrier is constant and unmodulated. Mickey is saying
>>that the duration of tc affects the bandwidth of the
>>transmitted signal. I have a big problem with this.
>>What is the physical process by which this happens?
>>During tc, you have an RF oscillator running at a
>>fixed frequency and amplitude. Each cycle of the sine
>>wave looks just like the one before it and just like
>>the one after it. So what is the connection between
>>duration and bandwidth? I just don't see it. If the
>>duration of tc affects bandwidth, how is that
>>physically produced?

First, what K5MC and AB0WR have been trying to describe is a periodic function. In other words, a keying waveform (i.e. a gate function) where the distance between the rising and falling edges ARE related by the keying speed used.

What you are describing is a keying waveform where the rise and fall times are non-periodic, i.e. NOT RELATED, and would require an analysis using step functions only.

Also, you are confusing time and frequency. The fact that a spectrum analyzer may show increased power in the sidebands at the start and end of a pulse doesn't tell you what those frequencies are or how they are energies are related. So be careful in describing the time related power and the frequency related power.

Here is a conundrum for you. You are saying the length of the pulse should have no effect on the sideband frequencies generated, only the rising and falling edges. This means the bandwidth would be constant out to about 120 wpm with 5 ms rise and fall times, i.e. when the pulse "width" would become zero. Yet even W8JI admits that at some higher speed the "percentage" of the rise and fall times become a significant portion of the pulse and therefore the bandwidth becomes dominated by the periodic analysis. I believe he indicates this occurs at around 50 wpm with 5 ms rise and fall times. This means that the transfer function would require at least two terms that describe bandwidth, some increasing and some decreasing (or remaining constant). They would cross over at about 50 wpm.

Can anyone do the math that describes this?

Jim
WA0LYK
 
RE: Bandwidth versus Keying Speed  
by W8JI on May 31, 2007 Mail this to a friend!
Since I can't seem to get the theorists to actually measure the bandwidth of a transmitter, I've measured it for them.

Please review this new page on my website:

http://www.w8ji.com/occupied_bw_of_cw.htm

These measurements were made with currently certified equipment that directly measures occupied bandwidth.

CW speed does NOT affect the occupied BW of a CW transmitter unless it changes the rising and falling edges of the waveform.


73 Tom

 
RE: Bandwidth versus Keying Speed  
by W8XR on May 31, 2007 Mail this to a friend!
Mickie,

Thanks for the Lahti reference - I'll see if I can find a used one (the retail is $117...) for additional reading.

My complaint with this reference and your general comment about other experts is that they don't provide an explanation of _why_ this should be the case - they merely corroborate your counter-intuitive assertion (or vice-versa.)

In order to make sense of the problem, I really need to have some concrete connection between theory and real systems. In many mathematic systems (at least the ones a typical engineer is likely to run across) you can make some exemplar transformations between formulae and the real world that they purport to model.

For example, a model of the operation of an inductor or oscillator feedback system describing electrons moving and accumulating and standing still provides a useful connection between the math used to describe the systems and the behaviour of the systems themselves. I'm sure as an educator, you appreciate the value of a good physical model to get your point across.

There should be such examples, or even some appropriate metaphors, that would help illustrate your assertions here.

Since many (perhaps most) hams will not be willing to dive into the math, it would be more effective for you to develop the math into some kind of physical model that they (we) can better understand.

Of course this is more about philosophy of science and epistomology (and pedagogy) than bandwidth... So, I'm going to quit, for now, disagreeing with your conclusions, as well informed as they may be.

Thanks to everyone for the broad and thought provoking comments, particularly those of you who illustrated my arguments better than I did!

Mark

 
RE: Bandwidth versus Keying Speed  
by W8XR on May 31, 2007 Mail this to a friend!
Tom,

Great real-world illustration!

Mark
 
RE: Bandwidth versus Keying Speed  
by AB0WR on May 31, 2007 Mail this to a friend!
K5MC:

Mickey,

You used a square wave for your analysis. Shouldn't you be using a gate function instead?

Use of a square wave assumes positive and negative peaks imposed as modulation on the carrier. A gate function would just be turning the carrier on and off which is what CW does.

It think you will get the same conclusion but the actual bandwidths may wind up being a little different. I've worked out the convolution of the gate function and the carrier graphically but I haven't yet finished the math or doing any actual calculations (too many things like the yard needing mowing and getting some sleep at night gets in the way!). I will keep working on them. My graph shows that you just get the sampling function waveform at the +/- carrier frequencies.

It would look to me like you would have a couple of terms involved. 1) if A is the amplitude of the pulse, tau is the length of the pulse, and T is the period between pulses then you would have a term like
(A * tau)/T. 2) you would also have a term that looks like
[sin (n * w * tau)/T] / [(n * w * tau)/T] where n is the number of the harmonic.

In other words the second function would be a sinx/x type of function with x being (n * w * tau)/T.

I'll get this all worked out sooner or later.

I know you pointed this out earlier but people seem to keep mixing up the time domain with the frequency domain. That is an easy thing to do. But once you have done a Fourier transform of a time domain function you lose the "time" placement information and everything gets shifted into the frequency domain.

In other words, in the frequency domain there is no "leading edge" or "trailing edge" of a pulse at a certain measureable point in time. There is only the pulse width and pulse period as "constants", if you will. Their unit is in seconds but all math in the frequency domain is done with respect to frequency in Hz and not time in sec so time is no longer a variable of concern in the frequency domain.

If the pulse width or period changes it will change the fundamental frequency w0, and the amplitude of the all the frequency components that make up the signal. But you still won't be able to tell where *in time* this all occurred.

For those that are interested, the actual rise time (or fall time) of a pulse really only tells you the bandwidth of the system response, i.e. how big "n" above can be. What you wind up with is a relationship that is basically
bandwidth * rise-time = pi or, for our purposes
bandwidth = pi/rise-time.

In other words the longer the rise time the lower the bandwidth the system has and this means the system will pass fewer harmonics of the fundamental frequency. A shorter rise time indicates that more harmonics can be passed. In the limit, as rise-time goes to zero, you wind up with a system that has infinite bandwidth. Using the relation above, a system which passes a square wave with a rise time of 5msec (.005sec) has a bandwidth of about 625hz. This means you can pass up to about 25 harmonics of a waveform with a fundamental frequency of 12.5hz (30wpm). I believe Mickey calculated 20 harmonics needed to reach the FCC bandwidth definition so a system with a 5ms rise time will be sufficient.

As Mickey pointed out there will be harmonics present out past his 20th harmonic. They may even be large enough to be seen on a spectrum analyzer. But you shouldn't see very many out past the 25th harmonic because of the system bandwidth limit.

If you take the transmitted bandwidth to include all harmonics that can pass through the system then you may very well take the bandwidth to be about 625hz for a CW signal. This seems to be a little excessive, however, for very slow keying speeds which have a much smaller fundamental frequency -- e.g. 5wpm with a 2hz fundamental would be able to get about 150 harmonics passed. The amplitude of the higher harmonics would probably be too small to be seen.

This also leads to the conclusion that 5ms rise time may very well be too long (i.e. the bandwidth may be too limited) to work well with faster keying speeds. Too many of the harmonics will begin to disappear to allow a good "perception" of when a pulse has actually been sent. That could very well be why some on here have said the "harder" keying pulse works better. The system providing the "harder" pulse would have a wider bandwidth (i.e. a shorter rise-time) and would pass more harmonics of the faster keying pulses allowing a better perception of the pulse.

I didn't mean to write a dissertation. I apologize for the length of the post. Guess I had a lot to say.

73,

tim ab0wr
 
RE: Bandwidth versus Keying Speed  
by W8JI on May 31, 2007 Mail this to a friend!
Tim,

Unfortunately the measured occupied BW of a transmitter, either by using a receiver or a spectrum analyzer capable of measuring occupied BW, does not change with keying speed unless the keying speed affects the slope of the rise and fall.

See:

http://www.w8ji.com/occupied_bw_of_cw.htm


73 Tom
 
RE: Bandwidth versus Keying Speed  
by KE3HO on May 31, 2007 Mail this to a friend!
WA0LYK: << What you are describing is a keying waveform where the rise and fall times are non-periodic, i.e. NOT RELATED, and would require an analysis using step functions only.

Also, you are confusing time and frequency. >>

Jim,

I am talking about the very same keying waveform that Mickey is talking about. A rising waveshape that is constant at all keying speeds, a steady state, followed by a falling waveform that also is constant at all keying speeds.

No, I am not confusing time and frequency. I do not believe for 5 ms that the keying speed affects the bandwidth of a CW transmitter. At the same time, I don't think Mickey is a fool of any sort. I have been trying to understand his analysis, and I was simply wondering if his "power bandwidth" might be some time weighted function - for example, like watt-seconds - key down for 1 second at 100 watts and you have 1 watt-second of power. If the "power bandwidth" somehow integrated the power at each frequency over the duration of the signal, then I could then see some connection between this "power bandwidth" and keying speed. Even if that is true, it only points to the fact that as keying speed increases the total watt-seconds that you transmit decreases. The power in the sidebands remains unchanged with keying speed, but the power in the sidebands becomes a more significant portion of your total watt-seconds as keying speed increases. Still, the bandwidth of the transmitted signal remains unchanged. Tom's measurements, along with others that he has cited here, show that.

73 - Jim
 
RE: Bandwidth versus Keying Speed  
by WB2WIK on May 31, 2007 Mail this to a friend!
There has to be a relationship between sending speed and bandwidth.

I know there's a relationship between the speed I drive my car and it's width -- which explains why I can fit through a tollbooth lane at 10 mph just fine but when I try it at 100 mph, the car doesn't fit.

:-)

WB2WIK/6
 
RE: Bandwidth versus Keying Speed  
by KE3HO on May 31, 2007 Mail this to a friend!
<< I know there's a relationship between the speed I drive my car and it's width -- which explains why I can fit through a tollbooth lane at 10 mph just fine but when I try it at 100 mph, the car doesn't fit. >>

Actually, it isn't your car that changes. The faster you drive, the smaller everything outside of your car gets. That's why when you drive faster you reach your destination soon - you have less distance to travel.

:-)

73 - Jim
 
RE: Bandwidth versus Keying Speed  
by AB0WR on May 31, 2007 Mail this to a friend!
w8ji:"CW speed does NOT affect the occupied BW of a CW transmitter unless it changes the rising and falling edges of the waveform."

w8ji:"Unfortunately the measured occupied BW of a transmitter, either by using a receiver or a spectrum analyzer capable of measuring occupied BW, does not change with keying speed unless the keying speed affects the slope of the rise and fall."

Rather than telling us we are wrong you would be better advised to figure out why the CW signal from a 751a does not match what theory predicts.

Trust me, I have been down this road many, many times. The math is correct. Anyone with an audio program like Cool Edit can generate a square wave and use the frequency analysis window to see the odd-order frequency components making up the square wave. Modulation of a carrier, either by a linear system such as one using a Gain Transfer function or by a non-linear system such as a FET mixer, only shifts these frquency components to being sidebands around the +/- carrier frequencies. Again, the math is correct, it just doesn't lie.

Similarly, the slope of the rise time does not generate any frequency components. The slope of the rise time only indicates the bandwidth of the system passing a square wave or generating a square wave. As the slope approaches vertical it only indicates a system with a wider bandwidth and as the slope gets more horizontal it only indicates a system with a narrower bandwidth. The slope itself generates nothing.

A CW key closure is either on or off. That is a step function if it happens once (i.e from off to on), it is a gate function if the transition happens regularly (i.e. off to on to off to on .....). That gate function generates a waveform that has frequency components that basically go on to infinity. Once you get high enough in the harmonic order the amplitude approaches zero but never quite gets there. That is what generates all the frequency components.

If the system connected to that CW key winds up with a waveform that has a slope then it is indicative of a bandwidth limited system. If you wish I can email you the Fourier analysis that shows this. That is all that the slope tells you, nothing more and nothing less.

I have looked at the spectrum graphs you show. I'm not even sure where to begin analyzing them. The first display doesn't even begin to show any of the individual frequency components involved in a square wave. For a 10hz signal you would have frequency components at 10hz, 30hz, 50hz, 70hz, etc. First off, it appears that you did a 90sec collection of data using a 10hz resolution. I suspect that the frequency jitter of the PLL in a 751a over 90sec would be enough to smear the 10hz spaced frequency elements of the CW signal all over the place. It would either make the frequency output look like a continuous spectrum instead of fixed elements or it would leave the spectrum analyzer missing important elements on which to base the bandwidth calculation. I believe the 751a has a 10hz step built into its oscillator which would confirm this assumption. Sometimes a specfic frequency component might look like it is at 10hz and the next instant be at 20hz -- and that is assuming you have a perfectly stable oscillator in your spectrum analyzer that doesn't make the smearing even worse.

This is further confirmed by your displays for 25 dots per second and for 40 pulses per second. The harmonics in the first would be at 25hz, 75hz, 125hz, etc. The low side of the display shows approximately this but at least one frquency component is missing. The high side doesn't show any of these close in elements. For a 40hz square wave the harmonics in a square wave would be a 40hz, 120hz, 200hz, 280hz, etc. This is far enough apart that the jitter in the 751a along with your resolutino would tend to establish a fixed location for some of the frequency components. That is why the 40 dots per second display shows a pretty good display. It's actually surprising that the occupied bandwidth for a 40 dots per second display is not wider than 500hz when the calculated bandwidth for a 12.5hz square wave is 525hz. This leads me to believe that the rise time of the 751a is actually longer than 5ms indicating a bandwidth restricted to something less than 625hz.

Bottom line? I'm not sure I would trust your spectrum analyzer to measure anything less than a 400-500hz bandwidth from a 751a transmitter. There are too many frequency jitter issues at the low speeds we are speaking of to insure that a proper measurement is being taken. I would believe you if you said that a 400-500hz bandwidth is the lowest you can measure. But that wouldn't make the math wrong in any way.

tim ab0wr
 
Bandwidth versus Keying Speed  
by KX0R on May 31, 2007 Mail this to a friend!
Perhaps it would clarify this discussion to remember that we don't hear "power bandwidth". We hear clicks, which are brief sounds associated with the sidebands produced by the transitions of a keying-modulated signal.

Regardless of what type of receiver we have, regardless of the filter, most of us listen with ears several khz wide. What we hear off-frequency from a clicking signal is something derived from those sidebands caused by the too-fast rise and fall of the keyed signal. In clicks we hear a mixture of the heterodyned click-sideband frequencies, receiver distortion products, intermod products, filter ringing, AGC effects, and numerous other transient byproducts. If the clicking signal is strong and the signal we wish to hear is weak, the effect on our relatively wideband ears and brain is severe. We do a lot of brain processing when we copy CW, and clicks from an interfering signal screw it up.

We don't really hear power bandwidth. I think that the author is correct that power bandwidth goes up with keying speed, for a constant modulation shape - but this is not very relevant when we're on the radio. The FCC's defintion is close to a power bandwidth definition, but that's not what we really care about on the bands when we're trying to copy a weak signal through key-click QRM.

W8JI is also right that the bandwidth (semi-instantaneous power bandwidth, not power bandwidth, fuzzy definition) is determined by the modulating function of the keying. Tom is talking about what exists on the spectrum (frequency domain) during the rise or fall of a keyed signal. What we hear with our wide-bandwidth ears is a whole bunch of almost instantaneous, complex junk that hinders our ability to concentrate on another station. This junk is much worse as the rise and fall times decrease.

Whether copy of high-speed signals is easier if they have faster (clicking) edges will be debated forever, but I think that W6TH is right that the sharp keying is easier to copy when the code speed is up high (with all its devastating clicks and QRM out several khz or more).

I have a switch for rise and fall time on the cathode keyer for one of my rigs. It's an RC circuit - technically imperfect. If copy is rough I sometimes sharpen my keying.

Every CW operator should look at his keyed output with a scope and decide if it represents what he wants to send all over the world.

You can also listen for clicks with a separate receiver, with your transmitter on a dummy load and minimal coupling to the receiver. The receiver must not be overloaded, and the AGC should be off. You can hear your clicks as you tune off-frequency with a narrow IF filter. It's easy to hear the clicks change as you make adjustments to your transmitter keying. If you get your rise and fall times longer than about 5 ms, you won't hear many clicks. The debate for all of us is whether keying like 1 or 2 ms is desirable, easier to copy through noise and QRM, etc. If you have a memory keyer, you can do tests to help decide for yourself. Some of us in the QRP ranks have been debating 1 or 2 ms keying vs the 5 ms "standard". A lot of folks think that sharp keying has an advantage and is "justified" with QRP. I think anything well under 2 ms is rude, unless you're a real fast op.

What we really need here is a reasonable compromise between theory and practical reality. A keyed CW signal with moderate shaping, even by an RC-derived modulation device, will greatly reduce interference caused by uncontrolled or defective shaping. It might be true that we need keying that is bit sharper, as well as a wider receiver filter, if we go real fast.

This is a real interesting topic, and thanks to the various super-sharp minds who have jumped into the fire here.

 
Bandwidth versus Keying Speed  
by KX0R on May 31, 2007 Mail this to a friend!
Before long, the leading manufacturers of HF/CW transceivers will offer features for control of the CW keying modulation. It would inexpensive to offer rise and fall times that are mathematically derived. These times could optionally track the keying speed, so the instantaneous bandwidth of the signal would be more nearly ideal.

These features might be attractive to operators who take pride in the quality of their signals. We certainly don't need thousands of powerful rigs with poor engineering filling our spectrum with nasty sidebands.

Newer rigs like the Elecraft K3 might be able to offer keying control features with only a firmware upgrade, since the DSP is in the signal path on transmit. Every cool new feature is an inducement to buy!
 
RE: Bandwidth versus Keying Speed  
by SM0AOM on May 31, 2007 Mail this to a friend!
I would recommend a through study of the
CCIR (ITU-R) Recommendation SM.328-10
"Spectra and Bandwidth of Emissions".

This Recommendation, as expected, quotes a "necessary bandwidth" for an A1A emission of K*B where K is the "hardness factor" of the telegraph signal elements (K= 3 or 5), and B is the modulation rate in Bauds.

Also, a semi-empirical expression for the A1A "occupied bandwidth" at the 1 percent out-of-band power level of L = B*((1/(0.05+a))-1)[Hz] is shown. "a" is the rise or fall time of the shortest signal element expressed as a fraction.

Note that all bandwidths are proportional to B.

"Plugging in" actual numbers for the IC-751 as read from the oscilloscope photo in the QST Jan 1985 review,(http://www.classicicom.com/product_reviews/pr8501.pdf)and taking the rise and fall times as the shortest of the asymmetrical envelope transitions (tr)about 3 ms, at a keying rate of 8 WPM or 6,66 baud (dot length of 150 ms)would result in a "necessary bandwidth" of 5 * 6,6 or 33 Hz and an "occupied bandwidth" of about 90 Hz.

Judging from the spectrum plots at http://www.w8ji.com/occupied_bw_of_cw.htm
the calculated "necessary bandwidth" of the IC-751 corresponds well to the main lobe width that can be seen on the 10 Baud (or dps) plot. The primary cause for the much wider "occupied bandwidth" appears to be deviation from the optimum Gaussian shape and the overshoot at the leading edge.

The ITU formulas corresponds also very well to actual spectral measurements made on ship's radiotelegraph transmitters by former colleagues at ITT/Standard Radio and Swedish Telecom Radio in the mid 70's. At that time type acceptance specifications often used the CCIR Gaussian keying function as the norm, and manufacturers became hard pressed to make equipment that had sufficiently good keying properties in order to present acceptable adjacent channel interference levels.

In the era of the DSP-based A1A or CW transceiver, it should not be too difficult to design adaptive keying shaping methods so that the ratios between "occupied" and "necessary" bandwidths are kept at a minimum.

The "bottom line" of this discussion may be that the amateur radio manufacturers should look into specification and design practices that the professionals accepted decades ago.


73/

Karl-Arne
SM0AOM

 
Bandwidth versus Keying Speed  
by K5MC on May 31, 2007 Mail this to a friend!
AB0WR: You used a square wave for your analysis. Shouldn't you be using a gate function instead? Use of a square wave assumes positive and negative peaks imposed as modulation on the carrier. A gate function would just be turning the carrier on and off which is what CW does.

K5MC: Now suppose our keying waveform is changed from the very good one described above to one having zero rise and fall times. "Square-wave" keying is quite a bit easier to examine mathematically than sinusoidal keying and it will yield a "worst-case" value of power bandwidth for a given speed. (Quoted from my article directly under Figure 1)

Tim, I apologize for the confusion. I thought everyone would understand that the "square-wave" keying waveform I described in my article was similar to my "sinusoidal" keying waveform shown in Figure 1 except that the rise and fall times of my "square-wave" keying waveform are zero. What I have been calling "square-wave" keying from the very beginning is exactly the same waveform as the classic rectangular (or gate) pulse train (as first mentioned by AB0WR) of constant amplitude (1 V in my calculations) with a pulse width "a" and a pulse period T (and a/T = 0.50 at both 2.4 wpm and 30 wpm). In other words, my "square-wave" keying waveform is equal to 1 V 50% of the time and it is equal to 0 V the other 50% of the time. (In hindsight I should have included a second figure in my article showing my "square-wave" keying waveform.)

As I posted earlier, the trigonometric form of the Fourier series for the 2.4-wpm and 30-wpm "square-wave" keying waveforms are given by s1(t) and s2(t), respectively, as follows:

s1(t) = 0.5 + (2/pi)[cos(2 pi t) - 1/3 cos(6 pi t) + 1/5 cos(10 pi t) - . . . ] volts

s2(t) = 0.5 + (2/pi)[cos(25 pi t) - 1/3 cos(75 pi t) + 1/5 cos(125 pi t) - . . . ] volts

Compare the two equations above with the "classic" square pulse periodic signal s3(t) that has an amplitude of plus or minus 0.5 V (therefore zero average value) with a fundamental frequency of 1 Hz:

s3(t) = (2/pi)[cos(2 pi t) - 1/3 cos(6 pi t) + 1/5 cos(10 pi t) - 1/7 cos(14 pi t) + . . . ] volts

We note that s3(t) has zero average (DC) value because it only includes harmonically-related cosine terms and the average value of each cosine wave is zero. However, both s1(t) and s2(t) include the factor 0.5; in other words, the average or DC value of s1(t) and s2(t) is 0.5 V. Notice that s1(t) = 0.5 + s3(t). That is, my 2.4-wpm "square-wave" keying waveform is simply s3(t) with a constant 0.5 V term added to it. To change from 2.4 wpm to 30 wpm, each of the frequency coefficients in the cosine terms in s1(t) are multiplied by 12.5 to obtain the Fourier series for the 30-wpm "square-wave" keying waveform because 30/2.4 is equal to 12.5.

By the way, I promise you that if you properly set up a waveform generator to produce a square pulse periodic signal having an amplitude of plus or minus 0.5 V and a period of 1 second (by looking, for example, at the signal in the time-domain on an oscilloscope), you will see the discrete-line (magnitude) spectrum on a modern spectrum analyzer as implied by the Fourier series for s3(t) above. That is, the spectrum analyzer will display the same amplitude values (within experimental error) at the proper frequencies as indicated in the s3(t) equation. For example, if the vertical display of the analyzer is set on a linear scale, the amplitude of the seventh harmonic component (7 Hz) will be only 1/7 that of the fundamental frequency component (1 Hz). If the vertical display of the analyzer is set on a log scale rather than a linear scale, then you will see the following relationship between the fundamental and seventh harmonic components:

20 log (1/7) = -16.9 dB

That is, the amplitude of the seventh harmonic is 16.9 dB "down" from the fundamental frequency component.

How do I know all of this? Because I have done it in the laboratory where I teach! For example, I frequently use an HP 3561A "Dynamic Signal Analyzer" in our electric machinery/power systems lab to examine the spectrum of such signals as the exciting current drawn by an unloaded power transformer. I have also used the spectrum analyzer capabilities of the HP 8920A in the communications lab at my school. As I said in one of my earlier posts, spectrum analyzers are based upon Fourier analysis (Fourier series, Fourier transforms, FFTs, etc.). It helps if the person using the spectrum analyzer has a good understanding of Fourier analysis!

Now if you believe that the equations for s1(t) and s2(t) above are correct for my "square-wave" keying waveforms at 2.4 wpm and 30 wpm, then it should be fairly easy for me to convince you the rest of the way! The CW signal that results from these keying waveforms is found by multiplying either s1(t) or s2(t) by an everlasting sinusoid. For example, the 2.4-wpm CW signal as a function of time is

s1(t) * cos (2 pi fc t) where fc is the carrier frequency.

We can now use fairly simple algebra and trigonometry to determine the frequency-domain components of this CW signal. The frequency components of this 2.4-wpm CW signal will include the carrier term at the frequency fc, the first pair of sidebands located plus and minus 1 Hz from the carrier, the second pair of sidebands (which correspond to the third harmonic component in s1(t)) located plus and minus 3 Hz from the carrier, and so forth. The frequency components of the 30-wpm CW signal will include the carrier at fc, the first pair of sidebands located plus and minus 12.5 Hz from the carrier, the second pair of sidebands (which correspond to the third harmonic component in s2(t)) located plus and minus 25 Hz from the carrier, and so forth.

Finally, the average powers for the various frequency components are calculated as I described in my comments posted late last night and the definition of power bandwidth gives you the final results for the "square-wave" keying waveform that I included in my article.

In closing this round of comments, let me say a few things that perhaps I should have emphasized more in my article. I used the example of "square-wave" keying to further illustrate the point that the power bandwidth does vary with sending speed, along with the fact that the rise/fall characteristics of the keying waveform are also very definitely a factor. There is no doubt that the key clicks that would be generated by such a keying waveform would be horrendous. The FCC addresses the problem of key clicks in Part 97 by such statements as "Emissions outside the necessary bandwidth must not cause splatter or keyclick interference to operations on adjacent frequencies." The FCC understands (just as I do) that the definition of occupied (or power) bandwidth does not adequately address the problem of key clicks caused by improper wave shaping. I've repeatedly said that the definition of occupied bandwidth only means exactly what it says! However, I think it would be nice if hams have some appreciation of how electrical engineers at the FCC (and other electrical engineers, whether in academia or in the "real world") calculate or measure the "occupied" or "power" bandwidth of a CW signal. To be honest, at times the technical comments posted in this thread have made me cringe at the idea of amateur radio in this country changing from the current "mode" approach to a "bandwidth" approach.

73, K5MC
 
RE: Bandwidth versus Keying Speed  
by AD5X on May 31, 2007 Mail this to a friend!
"Rather than telling us we are wrong you would be better advised to figure out why the CW signal from a 751a does not match what theory predicts."

Seems backwards to me. During my engineering career, I found that when I measured something other than what theory predicted, 99% of the time it was because the theoretical model was incorrect. You can certainly question the validity of the measurements, but you should also question the validity of the model.

Phil - AD5X
 
RE: Bandwidth versus Keying Speed  
by WR8Y on May 31, 2007 Mail this to a friend!
W8JI said:
""""Since I can't seem to get the theorists to actually measure the bandwidth of a transmitter, I've measured it for them.""""

I was wondering when someone would throw the calculators and books away and actually MEASURE SOMETHING!

W8JI said:
""""Please review this new page on my website:

http://www.w8ji.com/occupied_bw_of_cw.htm

These measurements were made with currently certified equipment that directly measures occupied bandwidth.

CW speed does NOT affect the occupied BW of a CW transmitter unless it changes the rising and falling edges of the waveform.

73 Tom """"

Awwwwwwwwwwwwwwwwww, ya beat me to it. I went to the trouble of dragging a radio and keyer into the shop and trying this was an RF Spectrum Analyzer. It was hard to make out anything below 1 kHz of width with our equipment - but I saw no difference between 5 and 40 WPM.

So, I then used the narrow filter in the TS830 to listen to another rig as I adjusted the speed - and the TS830's filters showed no difference in occupied bandwidth again, from 5 to 40 wpm.

Again, to quote you:
""""CW speed does NOT affect the occupied BW of a CW transmitter unless it changes the rising and falling edges of the waveform. """"

Exactly. But I think that egos and the willingness to argue are what this thread is about - not taking actual measurments!

Makr

 
RE: Bandwidth versus Keying Speed  
by W8JI on May 31, 2007 Mail this to a friend!
WR8Y Mark,

Thanks for taking the time to make some actual measurements. Many people take a hard position with verifying through experiment they are actually correct.

It was suggested I check my 751A to see why it does not follow some rules some people are applying.

The problem is I have measured at least a dozen different models of radios and NONE of them follow their theory either, and I know other people who have done the same.

I wonder what could really be wrong when measured results by multiple people on multiple pieces of gear using multiple methods consistantly do not match the prediction a few people present?

73 Tom

 
Bandwidth versus Keying Speed  
by W1YW on May 31, 2007 Mail this to a friend!
If the measurement does not match the prediction of well-known physics, hoary in origins, then either the measurement is in error or there are other factors being measured beyond what the PHYSICS states.

There is nothing wrong with the physics. Mickey knows what he is talking about.

73,
Chip W1YW
 
RE: Bandwidth versus Keying Speed  
by AB0WR on May 31, 2007 Mail this to a friend!
ad5x:"Seems backwards to me. During my engineering career, I found that when I measured something other than what theory predicted, 99% of the time it was because the theoretical model was incorrect. You can certainly question the validity of the measurements, but you should also question the validity of the model."

Please, this is nonsense. From designing trunk relays for 756 private branch exchanges to broadcast circuits using v-type amplifiers and a multiplicity of telephone cable types, when the circuit didn't behave the way the models showed it could be traced back to the physical implementation. From flat spring relays whose timings were out of spec to to improper options in the amps to cables contaminated with water, it wasn't the models that were wrong. If what you build doesn't do what your math say it should and your math follows established process then it can hardly be the model that is wrong.

The mathematics of the Fourier transforms, square waves, etc as well as modulation theory have been known since the turn of the 20th century.

If the physical implementation doesn't match the model then you need to look at the physical model.

Look at it this way. K5MC calculated the bandwidth of a 12.5hz signal to be about 525hz. That correlates *VERY* closely with the 490hz W8JI found for a 10hz signal.

The reason the bandwidth for the faster signals doesn't increase is because the system bandwidth is physically limited. The bandwidth of a 40hz signal should be much, much greater than a 12.5hz signal. Yet W8JI measures it to be about the same. Using the relationship that bandwidth * rise-time = pi that indicates a 40hz keying speed has the rise time of pi/bandwidth = 6.2 millisec for a 751a transmitter.

The slope of the waveform isn't what generates the harmonics, it is what *LIMITS* the number of harmonics the system can transmit. That seems to be what these displays are showing. Saying that slope of the waveform is what generates the harmonics is just plain incorrect. Saying that keying speed doesn't change the bandwidth is only correct for a bandwidth limited system where the input bandwidths are greater than the limited bandwidth the system can transmit.

What would be very interesting is to see what w8ji would measure for a 2 hz signal or even a 1hz signal. If the bandwidth still comes out to 500hz *then* it would be interesting to start digging into the 751a to see why.

WR8Y:"It was hard to make out anything below 1 kHz of width with our equipment - but I saw no difference between 5 and 40 WPM."

If it was hard to make out anything below 1000hz of width then how did you expect to make out something as small as a 10hz difference in the harmonic lobes? Considering that a 5wpm signal has harmonics at 6hz, 10hz, 14hz, etc. and a 40wpm signal has harmonics at 50hz, 83hz, 116hz, etc) seeing a 4hz or even a 33 hz difference between the lobes would seem to be a problem if it is hard to see anything below 1000hz width. Does your analyzer really have markings allowing reading down to the thousandths?

ALL:
I guess I would like for someone to explain to me just exactly how the math works that causes a 1hz square wave to have a bandwidth of 500hz when it is sent through a transmitter. You are saying that it does yet I have yet to see anyone explain it. I have the math to show that a rise time LIMITS bandwidth, it doesn't *cause* it. I don't have the math to show how a 1hz square wave can generate enough sidebands (at least out to the 249th harmonic) to have a 500hz bandwidth.

There are apparently enough people on here that believe this that *someone*, SOMEONE should be able to explain it mathematically.

And again, AGAIN, please don't tell me that the value of the slope of a square wave generates harmonics, it doesn't. It LIMITS the number of harmonics, it doesn't generate them! Anyone who wants the math showing this just let me know. I'll be glad to send it to you. Or you can go to http://zone.ni.com/devzone/cda/tut/p/id/2709, http://www.tek.com/Measurement/App_Notes/Technical_Briefs/bw_rt/55_18024_0.pdf, or even http://en.wikipedia.org/wiki/Rise_time for a description of how rise time indicates a bandwidth limited system.

So, is there anyone on here who can do more than quote the statement that "the slope of the rise time generates the bandwidth"? Is there anyone who can show the math for how a 1hz square wave can generate a 500hz bandwidth?

tim ab0wr
 
Bandwidth versus Keying Speed  
by K5MC on May 31, 2007 Mail this to a friend!
Below is an email I received from W7AY, along with my initial response. As long as Chen is OK with my posting his email messages to eham, I will keep everyone informed.

73, K5MC


Chen W7AY,

Thanks very much for your message. I will definitely post your message below along with my return comments.

The fact that you studied under Bracewell certainly gets my attention! I will try to find a copy of Bracewell's book in my school's library. Unfortunately, I've never obtained a personal copy of it.

While I'm trying to do that and look over your details below, please let me know exactly what your definition of bandwidth is. At one point you refer to the "effective" bandwidth. Please let me know in a precise way what you mean by the "effective" bandwidth.

In referring to your J2A signal below, you say that "the effective bandwidth does not change by much either." Can you be more specific (how much more as
a function of speed?) and, again, what is your definition of "effective" bandwidth? I am particularly interested if you can tell me the values of the 99% power bandwidth for your J2A signal at different speeds. (BTW, the keying waveforms in my article employed proportional spacing at both 2.4 wpm and 30 wpm. I'm assuming that your J2A signal does likewise.) From an English language point of view, the fact that you admit that the "effective" bandwidth does increase with speed (even if not "by much"), then it appears to me that you must also say that the sending speed is a factor in determining the "effective" bandwidth of your J2A signal.

Turning to my examples now in my eham article in which I calculated the 99.1% power bandwidth, do you disagree with any of my numerical results? That is, based upon the keying waveforms that I assumed, along with the
definition of "power" bandwidth that I quoted from Couch's textbook (which is essentially equivalent to the FCC's definition of "occupied" bandwidth), do you disagree with my results?

I'm looking forward to your response.

73, Mickey K5MC



----- Original Message -----
From: "Kok Chen" <chen@mac.com>
To: <k5mc@arrl.net>
Sent: Thursday, May 31, 2007 3:29 PM
Subject: Re: Bandwidth versus Keying Speed


> Hi Mickey,
>
> I am replying to your article by email rather than on eham for various
> reasons...
>
> Imagine that we build a wave-shaped stream of dits from scratch.
>
> Let's start with a "prototype" wave-shaped pulse.
>
> The pulse can be constructed from a single square pulse that is convolved
> with a window function (which is narrower than the square pulse).
>
> From the Fourier Duality theorem, the Fourier transform of the shaped
> pulse must therefore be the product of the Fourier transform of the
> square pulse and the Fourier transform of the window.
>
> I.e.,
>
> F( p*w ) = F( p ) F (w )
>
> where * is the convolution operator, and F() is the Fourier transform, p
> is the time waveform of a single square pulse and w is the time waveform
> of the wave-shaping window.
>
> The transform of the single pulse is of course a sin(x)/x function.
>
> I will use a Gaussian window (since its Fourier transform is also a
> Gaussian and it is easier to describe things).
>
> So, the transform of the resultant shaped pulse is the product of a
> Gaussian and a sin(x)/x function.
>
> Notice that for any smooth function that you use as a window, it's
> Fourier transform will fall faster than the envelope of the sin(x)/s
> function -- i.e., for a reasonable wave-shaping, the Fourier transform of
> the Gaussian falls off faster than 1/f where f is frequency.
>
> Ergo, it is the wave-shaping function that is what governs the bandwidth
> of the shaped pulse, it is not the pulse width.
>
> Now, a sequence of dits is just a convolution of a comb of Dirac deltas
> with the fundamental shaped pulse.
>
> In his classic Fourier Transform book, Bracewell had called a comb of
> Dirac deltas to be a "Shah" function and showed that the Fourier
> transform of a Shah is just another Shah function (i.e., the Gaussian is
> not the only function that is its own transform).
>
> (I was fortunate to have Bracewell as a professor in both a Fourier
> Transform and an Interferometry grad class back at Stanford many decades
> ago).
>
> Again, from the Fourier Duality statement, the spectrum of a series of
> dits is just a product of the Fourier transform of the prototype shaped
> pusle and a comb in the frequency domain. Again, the spectrum of the
> "window" predominates and knocks out all the higher frequency components
> of the comb.
>
> I.e., as a first order approximation, the envelope of the spectrum of a
> series of dits is just the Fourier transform of the wave shaping window.
>
> In this sense, W8JI is correct in stating that it is rise and fall times
> that matters (i.e., it is the window function that matters) since the
> rise and fall times are defined by the window shape as I describe here.
>
> I have implemented CW transmission by using J2A modulation (instead of
> using A1A modulation) in a software modem for the MacOS. For the
> waveshaping function, I had used a modified Blackman window. You can see
> the spectrum of a series of dits here:
>
> http://homepage.mac.com/chen/cocoaModemPage/UsersManual/cwManual/
> index.html
>
> Just scroll down to Figure 5.
>
> As theory predicts, by using the constant Blackman window (i.e., rise
> time and fall time left invarient), what happens to the spectrum as you
> change keying speed is that the lobes under the envelope change spacings,
> but the envelope itself does not change -- and thus the effective
> bandwidth does not change by much either. When you increase the keying
> speed, the lobes under the envelope will be wider spaced (since in the
> time domain they become closer to one another -- another factoid from
> Fourier theory). Until your keying speed becomes so fast that there is
> only a single lobe under the window's envelope -- at that point the Morse
> will sound very "soft" to the ear (but with Blackman windows, will not
> "ring.").
>
> Please feel free to post this to eham if you wish.
>
> Vy 73
> Chen, W7AY
 
Bandwidth versus Keying Speed  
by K5MC on May 31, 2007 Mail this to a friend!
AB0WR: Is there anyone who can show the math for how a 1hz square wave can generate a 500hz bandwidth?

Tim, I admit that I'm getting pretty confused trying to keep up with the comments from everyone. Can you give me a little more background on what you are talking about here?

73, K5MC
 
Bandwidth versus Keying Speed  
by K5MC on June 1, 2007 Mail this to a friend!
W8JI: See: http://www.w8ji.com/occupied_bw_of_cw.htm

Tom, I've looked at your spectrum plots. I have some questions and comments regarding your results.

1. Did you also use an oscilloscope and see the actual envelopes of the CW signals (the exact same CW signals as fed into your spectrum analyzer) as functions of time? If you didn't, I think you need to. Otherwise, you are assuming too much.

2. Based upon your oscilloscope observations, did your Icom 751A actually send dits uniformly at the rate of 40 per second? That's 96 wpm! I find it pretty hard to believe that an unmodified 751A can achieve that speed without some serious shortcomings in the output signal. I also wouldn't be too surprised if it had some difficulty when keyed at 25 dits per second (60 wpm).

3. If you send a uniform string of dits for a "long" time, then the magnitude spectrum that you would have to see on an ideal analyzer would be essentially discrete because such a signal would be, for all practical terms, a periodic signal. It's true that it would take an infinite amount of time to achieve a perfect discrete line spectrum, but the fact that your spectrum plots are clearly not discrete and the spectrum plots for the signals in my article are discrete means that we are comparing, to some degree at least, apples and oranges.

4. Continuing with my comments from #3, can you make some adjustments on your particular analyzer so that your display will be more like what it should be for a long string of dits? I see that you are sweeping over an identical range of 3 kHz for all three speeds. If it's possible on your particular analyzer, I think you need to reduce the frequency span below 3 kHz, particularly at the slower speeds. (However, I've got a feeling that 3 kHz might be the smallest span your analyzer allows, at least at 3.5 MHz.)

5. Since the frequency span of your analyzer is set to 3 kHz, and the 99% power bandwidth at 24 wpm is probably around 150 Hz for the 751A (assuming it has reasonably good keying characteristics), your span is well over 10 times what is needs to be to capture essentially all of the signal's spectrum. If you could decrease your span to 150 Hz or so, for example, you would see a spectrum that is much closer to what it really is (essentially a discrete line spectrum). As your analyzer's frequency span increases, its spectrum resolution decreases and that is a major problem in your results.

73, K5MC
 
RE: Bandwidth versus Keying Speed  
by W8JI on June 1, 2007 Mail this to a friend!
by K5MC on June 1, 2007

<<1. Did you also use an oscilloscope and see the actual envelopes of the CW signals (the exact same CW signals as fed into your spectrum analyzer) as functions of time? If you didn't, I think you need to. Otherwise, you are assuming too much.>>

Of course I've looked at the envelope! Looking at the envelope really doesn't yield much useful information other than when major changes in envelope shape occur. The things that cause adjacent channel problems can be very subtile, as you know.

The 751A starts to seriously modify the envelope at about 55 dits per second, but the only change at 40 dits per second is a small decrease in weight. The off time is a bit longer compared to on time, but the dot rate does NOT change and neither does peak envelope power.

I intentionally stayed well below the radio's speed limit.

<<2. Based upon your oscilloscope observations, did your Icom 751A actually send dits uniformly at the rate of 40 per second? That's 96 wpm! I find it pretty hard to believe that an unmodified 751A can achieve that speed without some serious shortcomings in the output signal. I also wouldn't be too surprised if it had some difficulty when keyed at 25 dits per second (60 wpm). >>

The 751A has a pretty fast rise and fall, and yes....it has no problems at all. It's my opinion radio manufacturers are crazy with speed limits and that's why keyclicks are such an issue. The bandwidth is horrable at any speed compared to necessary bandwidth.

<<3. If you send a uniform string of dits for a "long" time, then the magnitude spectrum that you would have to see on an ideal analyzer would be essentially discrete because such a signal would be, for all practical terms, a periodic signal. It's true that it would take an infinite amount of time to achieve a perfect discrete line spectrum, but the fact that your spectrum plots are clearly not discrete and the spectrum plots for the signals in my article are discrete means that we are comparing, to some degree at least, apples and oranges. >>

We are comparing what you predict and what actually happens Mickey, and respectfully that indeed is apples and oranges.


<<4. Continuing with my comments from #3, can you make some adjustments on your particular analyzer so that your display will be more like what it should be for a long string of dits? I see that you are sweeping over an identical range of 3 kHz for all three speeds. If it's possible on your particular analyzer, I think you need to reduce the frequency span below 3 kHz, particularly at the slower speeds. (However, I've got a feeling that 3 kHz might be the smallest span your analyzer allows, at least at 3.5 MHz.) >>

That setting depends on the assigned channel bandwidth, although I can manually override its control of span. The channel bandwidth really should be wide enough to see all the sidebands of the transmitter, and in this case I set it at 1kHz.

The analyzer BW is 10Hz, naturally requiring a very long sweep time. If I span 500Hz, the results are virtually identical. I've done that.

I think you are looking for the periodic frequency domain ripples that are predicted, and they do indeed occur IF the analyzer sweep is triggered in exact sync with the dot generator. Of course that does not change the occupied bandwidth, it remains essentially the same.

The only way I can change the occupied BW more than a few Hz from the ~500 Hz displayed is to change the rise and fall characteristics, not the speed.


<<5. Since the frequency span of your analyzer is set to 3 kHz, and the 99% power bandwidth at 24 wpm is probably around 150 Hz for the 751A (assuming it has reasonably good keying characteristics), your span is well over 10 times what is needs to be to capture essentially all of the signal's spectrum. If you could decrease your span to 150 Hz or so, for example, you would see a spectrum that is much closer to what it really is (essentially a discrete line spectrum). As your analyzer's frequency span increases, its spectrum resolution decreases and that is a major problem in your results. >>

Well, it has ten Hz resolution bandwidth now. Exactly how narrow does it have to be to display a 500Hz wide signal with reasonable accuracy? In my experience 2% of the transmitter's BW is pretty damn good.

I just let a 500Hz span with 10Hz selectivity run, and guess what? The same radio had 500Hz occupied bandwidth.

I really don't see what the problem is Mickey. I can duplicate the results using a Selective Level Meter that has peak power averaging, and a regular CW receiver with narrow filters pretty much agrees.

This pattern repeats from transmitter to transmitter. Some clicky Yaesus and a Ten Tec Omni C I tested have over 1kHz OBW and the bandwidth repeats at various speeds unless the speed affects the rise and fall shape or duration. They bother people on the air at ANY reasonable speed, I can hear them the same distance off frequency at any reasonable speed. They all have different bandwidths when the rises and falls are different times and shapes, but they all share in common the single fact bandwidth does not change substantially with speed.

You were openly critical of W9CF's abilities, but the fact is every single measurement I've ever made using good careful methods agrees 100% with W9CF and disagrees with Tim and your predictions.

Not only that some very experienced communications systems engineers, people I consider the top in the field (I've met about 5 people like that in the past 40 years) disagee with the way you and Tim are predicting bandwidth and agree with W9CF and others.

As a matter of fact if I syncronize the sweep trigger points with the dot generator time base, the picture on the analyzer looks exactly like the frequency domain Kevin predicts. This does not change the OBW that is measured, it simply changes the picture to make nulls and peaks appear.

If everyone else is wrong, why do direct measurements of at least a dozen rigs using multiple methods disagree with you and Tim? Are the other people AND the measurements all in error? If so why don't the actual systems, the receivers and transmitters, behave the way you predict on the air?

Why can I hear a FT1000MP or IC775DSP about the same distance away regardless of keying speeds? Why don't the clicks suddenly move in closer to the carrier frequency when only the speed is reduced?

73 Tom
 
RE: Bandwidth versus Keying Speed  
by AD5X on June 1, 2007 Mail this to a friend!
ad5x:"Seems backwards to me. During my engineering career, I found that when I measured something other than what theory predicted, 99% of the time it was because the theoretical model was incorrect. You can certainly question the validity of the measurements, but you should also question the validity of the model."

AB0WR: "Please, this is nonsense. From designing trunk relays for 756 private branch exchanges to broadcast circuits using v-type amplifiers and a multiplicity of telephone cable types, when the circuit didn't behave the way the models showed it could be traced back to the physical implementation. From flat spring relays whose timings were out of spec to to improper options in the amps to cables contaminated with water, it wasn't the models that were wrong. If what you build doesn't do what your math say it should and your math follows established process then it can hardly be the model that is wrong."

I'm sorry, but I disagree. You must consider that either the model OR the measurement (or both) can be the problem. My experience is with QAM digital microwave communications designs (4-256 QAM) and DWDM lightwave designs operating at 10gb/s. We often had advanced technology groups of engineers working to try to resolve the differences between our measurements and the models - and the problems were almost always with the models. Don't get me wrong - errors were also made in measurements. But normally it was the accuracy of the models that was at issue. Over time our models would get better, but then we would introduce more complex modulation systems, higher data rates, more power, etc and find that there were new unknowns that made the models inaccurate. When there is a discrepancy between measurement and theory, you must look at both and try to resolve the discrepancy. You have to assume that either could be wrong. Automatically assuming that one is correct and the other isn't can lead you into months of effort working on the wrong thing. I've seen this too many times.

I am certainly enjoying this thread. Who knows, maybe we'll all learn something.

Phil - AD5X
 
Bandwidth versus Keying Speed  
by W1YW on June 1, 2007 Mail this to a friend!
I'm sorry, but I disagree. You must consider that either the model OR the measurement (or both) can be the problem.

------------------------------

And again, you have those with the experience to disagree with this comment.

So let's push it further. Mickey has given a nice, simple (but elegant) analysis that establishes how extant physics reveals certain inherent bandwidth issues that relate to speed of transmission. He is NOT presenting this as a basis for testing the validity of the PHYSICS--no; he is presenting it as a guide for what to look for in APPLICATIONS.

Notice it is NOT presented as a PREDICTION of a THEORY. Why? Because the analysis includes no new physics.

Given that state, if you DON'T masure what Mickey SHOWS, then there are either ERRORS or UNCERTAINTIES in the measurement---or-- there are additional factors in the EQUIPMENT BEING MEASURED that go beyond the analysis being presented. In the latter, the ASSUMPTION being made is that no OTHER factors are affecting the MEASUREMENT.

IMO, hams would be better served for themselves if they used Mickey's analysis to understand the limits of measurement, and the transfer functions inherent to their equipment. That itself is interesting.


73,
Chip W1YW
 
RE: Bandwidth versus Keying Speed  
by WR8Y on June 1, 2007 Mail this to a friend!
WR8Y:"It was hard to make out anything below 1 kHz of width with our equipment - but I saw no difference between 5 and 40 WPM."

AB0WR: "If it was hard to make out anything below 1000hz of width then how did you expect to make out something as small as a 10hz difference in the harmonic lobes? Considering that a 5wpm signal has harmonics at 6hz, 10hz, 14hz, etc. and a 40wpm signal has harmonics at 50hz, 83hz, 116hz, etc) seeing a 4hz or even a 33 hz difference between the lobes would seem to be a problem if it is hard to see anything below 1000hz width. Does your analyzer really have markings allowing reading down to the thousandths?"

Did you read the rest of my post? I then resorted to using the 170 hz filter in the 830 while listing to a stream of dits - adjusting the speed from 5 WPM to 40 WPM. NO BANDWIDTH CHANGE!
 
RE: Bandwidth versus Keying Speed  
by W9AC on June 1, 2007 Mail this to a friend!
> http://www.w8ji.com/occupied_bw_of_cw.htm

If a picture is worth a thousand words, a well-documented spectrum plot is worth ten thousand.

Well done.

If Mickey's theory were correct, we should see at least *some* relevant level of increasing bandwidth as a function dits per unit of time, assuming all other variables remain constant as you have ensured -- even if (arguably) the spectrum analyzer mechanics do not completely track with mathematics.

Tom, one final test might be to temporarily disable ALC on the 751A to rule out the mid-speed ALC anomaly, just to satisfy any doubters.


 
RE: Bandwidth versus Keying Speed  
by AB0WR on June 1, 2007 Mail this to a friend!
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

w8ji:"If everyone else is wrong, why do direct measurements of at least a dozen rigs using multiple methods disagree with you and Tim? Are the other people AND the measurements all in error? If so why don't the actual systems, the receivers and transmitters, behave the way you predict on the air? "



w9ac:"> http://www.w8ji.com/occupied_bw_of_cw.htm

If a picture is worth a thousand words, a well-documented spectrum plot is worth ten thousand.

Well done.

If Mickey's theory were correct, we should see at least *some* relevant level of increasing bandwidth as a function dits per unit of time, assuming all other variables remain constant as you have ensured -- even if (arguably) the spectrum analyzer mechanics do not completely track with mathematics.

Tom, one final test might be to temporarily disable ALC on the 751A to rule out the mid-speed ALC anomaly, just to satisfy any doubters. "

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>


If you two would actually read what is being posted this is what you would find:

A square wave with a rise time of 5ms to 6ms indicates a system with a MAXIMUM bandwidth of 523hz 628hz. The rise time doesn't *generate* this bandwidth, it is a response to an *INPUT* signal. A signal with a smaller bandwidth will pass through relatively unaffected. A signal with a wider bandwidth will be limited to the system bandwidth while passing through the system.

You are shoving square waves at 10hz to 40hz, which should have bandwidths of 500hz and *GREATER*, into a bandwidth limited system (around 500hz to 600hz) and then saying that the keying speed doesn't determine the bandwidth of the keyed signal.

You are then extrapolating that to saying that *ANY* keying speed will have a 500hz bandwidth.

Do you see the disconnect? What you should be saying is that the system response limits the output response. Instead, you are trying to convince everyone that it limits the input.

If you put a keying speed of 1hz to 5hz into the system, both of which will have bandwidths of *less* than 500hz, do you really expect to still see a 500hz bandwidth output from the 751a?

If you want to show us something, show us how a string of dits at 2hz will generate a signal with a bandwidth of 500hz. Show us the math that shows that a 2hz square wave has a bandwidth of 500hz.

Mickey's analysis *is* correct. If you don't understand the inputs *to* the system you will never understand the outputs *from* the system. That fact that you have rise times on the outputs indicates that you have a bandwidth limited system reponse. If the input bandwidth is wider than the system response bandwidth you get exactly what Tom is showing in his displays. You have extrapolated that into saying that the system response will *ALWAYS* be that wide no matter what the input happens to be. Yet your displays only include inputs that are *wider* than the system response. Therefore you have not provided a full system test.

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
w8ji:"If everyone else is wrong, why do direct measurements of at least a dozen rigs using multiple methods disagree with you and Tim? Are the other people AND the measurements all in error? If so why don't the actual systems, the receivers and transmitters, behave the way you predict on the air?"
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Do they all have 500hz bandwidth outputs regardless of the input? Do they have 500hz bandwidths at keying speeds *LESS* than 10hz? You haven't shown us that yet. You are measuring the outputs of a bandwidth limited system using input responses with bandwidths equal to or greater than the system response and then are saying that the output response you see will *ALWAYS* be what you see regardless of the input. Show us that a system input at 2hz results in a 500hz bandwidth output and then we can actually discuss why that is.

tim ab0wr
 
RE: Bandwidth versus Keying Speed  
by W8JI on June 1, 2007 Mail this to a friend!
W9AC Paul,

I've watched the waveforms on the scope and even measured a Viking Valiant and a Globe Scout of all things.

It absolutely is not an instrument artifact since I've used multiple measurement devices.

It behaves this way on a simple real receiver.

It behaves this way on a Selective Level Meter.

It isn't ALC because it behaves this way on radios without ALC and at any power setting on radios with ALC. As a matter of fact my FT1000MKV's were sometimes set so the ALC wasn't active. Didn't make a difference in them because the hold time was long enough to stabilize the gain.

73 Tom



 
RE: Bandwidth versus Keying Speed  
by AB0WR on June 1, 2007 Mail this to a friend!
k5mc:"To be honest, at times the technical comments posted in this thread have made me cringe at the idea of amateur radio in this country changing from the current "mode" approach to a "bandwidth" approach. "

Me too. Using w8ji's and w9ac's claim that a cw keying waveform always has a 500hz bandwidth, regardless of how slow the keying speed is, and overlaying this on the ARRL's bandwidth segmentation plan, CW would always be restricted from using the narrow, 200hz bandwidth portion of the band. It would have to stay in the 1.5khz bandwidth portion and compete with all of the wider digital modes.

I would also like to point out that the analysis you received from the other ham speaking of the convolution of a comb input and a shaped window in the time domain is still nothing more than the classis Output(w) = Input(w)System-response(w) form of equation in the frequency domain. If the Input(w) is a true shaped comb input then that indicates a very wide bandwidth input (infinite perhaps?)together with a system response that is bandwidth limited. Of course the output response will be bandwidth limited. That is really all his analysis is saying.

On the other hand, if the Input(w) is a limited bandwidth signal that is smaller than the System-response(w) window, the System-response(w) window will have no affect at all on the Output(w).

Too many people here are trying to say that since the Output(w) response is bandwidth limited by the System-response(w) that the Output(w) response will *always* be the same bandwidth. They are ignoring the cases where the Input(w) signal has a lower bandwidth than the System-response(w) transfer function. It would seem that they are mistaking the system response bandwidth for both the input signal *and* the output signal and saying that they are all the same thing. That just isn't true.

Your (and the FCC's) definintion of the signal bandwidth puts a restriction of the bandwidth to be considered, even on a square wave with an infinite number (albeit progressively weaker) of harmonics. If that restriction results in the definition of a system input that is narrower than the system response function, the input should be seen in all its glory in the output, e.g. your analysis for a keying wave of 1hz speed. If a 1hz square wave keying waveform has a 99.1% power bandwidth of 42hz it should pass through a system with a 500hz system bandwidth response relatively unaffected. On the other hand, an input with a 525hz bandwidth (your 12.5hz square wave keying waveform) *will* be bandwidth limited to 500hz by the system response bandwidth window.

I would still like to see a spectrum analyzer display from Tom that shows the output bandwidth for a 1hz keying waveform. That would show the output response from an input signal that is narrower than the system response function. It will be very interesting to see if that would still show a 500hz bandwidth for the output response.

tim ab0wr
 
RE: Bandwidth versus Keying Speed  
by AB0WR on June 1, 2007 Mail this to a friend!
w9ac:"If Mickey's theory were correct, we should see at least *some* relevant level of increasing bandwidth as a function dits per unit of time, assuming all other variables remain constant as you have ensured -- even if (arguably) the spectrum analyzer mechanics do not completely track with mathematics. "

How do you expect the Output response to vary in bandwidth if the Input signal always has a bandwidth wider than the System-response bandwidth?

output(t) <-> Output(w)

Output(w) = Input(w)System(w)

If Input(w) is always wider than System(w) why would you expect Output(w) to change in any way?

That's really all Tom's displays are showing us - an Output response from Input signals with a wider bandwidth than the system can pass. Of course they will always show the same bandwidth -- that of the system response.

How do you extrapolate this to also claiming that Input signals with bandwidths less than the System bandwidth will also cause Output responses equal to the System bandwidth?


tim ab0wr
 
RE: Bandwidth versus Keying Speed  
by AB0WR on June 1, 2007 Mail this to a friend!
wr8y:"Did you read the rest of my post? I then resorted to using the 170 hz filter in the 830 while listing to a stream of dits - adjusting the speed from 5 WPM to 40 WPM. NO BANDWIDTH CHANGE!"

Exactly what did you expect to hear that would indicate a change in bandwidth?

Did you expect the sound you heard to change from a tone to a buzz if the bandwidth changed?

If what you heard didn't change, exactly how does that relate to the bandwidth not changing?

I would be very interested in knowing exactly what you would expect a change in bandwidth to "sound" like? Can you define what the different bandwidths would sound like if they, in fact, *did* change?

tim ab0wr
 
RE: Bandwidth versus Keying Speed  
by W8JI on June 1, 2007 Mail this to a friend!
Tim,

I know how to tune a receiver and listen to signal levels, and I know how to read an S meter.

I can hear the clcks exactly the same distance from the carrier at any speed so lon as I don't have a speed that changes the envelope rise and fall.

I know we are all uncomfortable with and disagreement that disputes what we believe, but that's just a fact we can't change.

Secondly, I reduced the speed to 4dps. That's pretty darned slow. The Occupied BW is 465 Hz. That's right in line with all the other measurements.

We can probably all look forever, but what Chen posted agrees with Kevin W9CF and many other people. Chen explains it well. Like W9CF, the measured data I get looks exactly like the predictions of W9CF and many other people.

Let me repost the eHam posting it so perhaps you can think about where you went wrong:

> Imagine that we build a wave-shaped stream of dits from scratch.
>
> Let's start with a "prototype" wave-shaped pulse.
>
> The pulse can be constructed from a single square pulse that is convolved
> with a window function (which is narrower than the square pulse).
>
> From the Fourier Duality theorem, the Fourier transform of the shaped
> pulse must therefore be the product of the Fourier transform of the
> square pulse and the Fourier transform of the window.
>
> I.e.,
>
> F( p*w ) = F( p ) F (w )
>
> where * is the convolution operator, and F() is the Fourier transform, p
> is the time waveform of a single square pulse and w is the time waveform
> of the wave-shaping window.
>
> The transform of the single pulse is of course a sin(x)/x function.
>
> I will use a Gaussian window (since its Fourier transform is also a
> Gaussian and it is easier to describe things).
>
> So, the transform of the resultant shaped pulse is the product of a
> Gaussian and a sin(x)/x function.
>
> Notice that for any smooth function that you use as a window, it's
> Fourier transform will fall faster than the envelope of the sin(x)/s
> function -- i.e., for a reasonable wave-shaping, the Fourier transform of
> the Gaussian falls off faster than 1/f where f is frequency.
>
> Ergo, it is the wave-shaping function that is what governs the bandwidth
> of the shaped pulse, it is not the pulse width.
>
> Now, a sequence of dits is just a convolution of a comb of Dirac deltas
> with the fundamental shaped pulse.
>
> In his classic Fourier Transform book, Bracewell had called a comb of
> Dirac deltas to be a "Shah" function and showed that the Fourier
> transform of a Shah is just another Shah function (i.e., the Gaussian is
> not the only function that is its own transform).
>
> (I was fortunate to have Bracewell as a professor in both a Fourier
> Transform and an Interferometry grad class back at Stanford many decades
> ago).
>
> Again, from the Fourier Duality statement, the spectrum of a series of
> dits is just a product of the Fourier transform of the prototype shaped
> pusle and a comb in the frequency domain. Again, the spectrum of the
> "window" predominates and knocks out all the higher frequency components
> of the comb.
>
> I.e., as a first order approximation, the envelope of the spectrum of a
> series of dits is just the Fourier transform of the wave shaping window.
>
> In this sense, W8JI is correct in stating that it is rise and fall times
> that matters (i.e., it is the window function that matters) since the
> rise and fall times are defined by the window shape as I describe here.
>
> I have implemented CW transmission by using J2A modulation (instead of
> using A1A modulation) in a software modem for the MacOS. For the
> waveshaping function, I had used a modified Blackman window. You can see
> the spectrum of a series of dits here:
>
> http://homepage.mac.com/chen/cocoaModemPage/UsersManual/cwManual/
> index.html
>
> Just scroll down to Figure 5.
>
> As theory predicts, by using the constant Blackman window (i.e., rise
> time and fall time left invarient), what happens to the spectrum as you
> change keying speed is that the lobes under the envelope change spacings,
> but the envelope itself does not change -- and thus the effective
> bandwidth does not change by much either. When you increase the keying
> speed, the lobes under the envelope will be wider spaced (since in the
> time domain they become closer to one another -- another factoid from
> Fourier theory). Until your keying speed becomes so fast that there is
> only a single lobe under the window's envelope -- at that point the Morse
> will sound very "soft" to the ear (but with Blackman windows, will not
> "ring.").
>
> Please feel free to post this to eham if you wish.
>
> Vy 73
> Chen, W7AY

What Chen describes above is precisely what appears when we look at the spectrum. Mickey and you are unfortunately not right on this one Tim.

73 Tom




 
Bandwidth versus Keying Speed  
by K5MC on June 1, 2007 Mail this to a friend!
I hope everyone will find these email messages between W7AY and myself to be of interest.

BTW, I appreciate some of the recent comments posted, particularly by Chip W1YW and Tim AB0WR, very much. There have been times during this thread when I have felt very lonely in trying to get my points across!

73, K5MC

Chen,

Thanks very much for your quick reply. I believe the end of this discussion
(at least the first phase of it) is now in sight. I am very happy to hear
you say that the results I presented in my article are "perfectly sound."
Regarding the "optimum" shaping factor for the keying waveform, I have no
doubt that my "sinusoidal" choice is not the optimum as you say. I was
careful to say it was a "very good" one, but with hindsight I probably
should have merely said it was much better than no shaping at all. I was
clearly thinking of the performance of the sinusoidal shape versus what I
called "square-wave" keying when I made that statement in my article.

I chose the sinusoidal shape primarily because I knew I could readily find
its Fourier series coefficients "exactly" by evaluating the integrals by
hand and then double checking my results using EXCEL. As I have some spare
time this summer, I might look at the other waveshapes you have mentioned
(raised cosine, etc.) and see how much difference there is in the 99% power
bandwidth at a given speed. Right now my gut feeling is that there is "not
much" (say, maybe 125 Hz for the "best" versus my 150 Hz at 30 wpm.)

Yes, I would very much appreciate a copy of VE3NEA's QEX article. I don't
suscribe to it and apparently everyone who has commented during this thread
are either in the same boat or they've forgotten about that particular
article.

Concerning your comment about what the "practical guys" are seeing on their
analyzers, I'm afraid I do disagree with you on that assessment at this
point. I believe that W8JI is simply being mislead by his analyzer! If you
will look at the spectrum plots that he presents at
http://www.w8ji.com/occupied_bw_of_cw.htm I think you will see what I mean.
I'm afraid the resolution of his analyzer is simply not great enough at 3.5
MHz to really see what's going on with the keying sidebands generated by
such a narrow CW/ASK signal as that produced by a string of dits at 24 wpm.

I've got to start teaching some classes today, but I will also see if I can
screw together some lab equipment that will actually show the keying
sidebands and the resulting "power" or "occupied" bandwidth as I described
in my article.

Thanks again very much.

73, Mickey K5MC



----- Original Message -----
From: "Kok Chen" <chen@mac.com>
To: "mcoxk5mc" <mcoxk5mc@bellsouth.net>
Sent: Friday, June 01, 2007 12:19 AM
Subject: Re: Bandwidth versus Keying Speed


> Hi again, Mickey,
>
> Please read the part last answer (No, you are **NOT** wrong) first and
> then you can read the top, HI HI.
>
> On May 31, 2007, at 9:16 PM, mcoxk5mc wrote:
>> In referring to your J2A signal below, you say that "the effective
>> bandwidth does not change by much either." Can you be more specific
>> (how much more as a function of speed?) and, again, what is your
>> definition of "effective" bandwidth?
>
> Basically, the "envelope" of the spectrum does not change. The only
> thing that changes is the spacing of the lines within that envelope. So,
> as you change the keying rate, the distribution of the energy _under_ the
> spectral envelope changes, but is upper bounded by the envelope itself.
> I.e., the envelope (i.e., a single pulse) is the upper bound of how wide
> the spectrum is.
>
>> I am particularly interested if you can tell me the values of the 99%
>> power bandwidth for your J2A signal at different speeds. (BTW, the
>> keying waveforms in my article employed proportional spacing at both 2.4
>> wpm and 30 wpm. I'm assuming that your J2A signal does likewise.)
>
> I don't design using 99% figures. IMO, it is much better to specify how
> many dB down at a certain frequency away.
>
> For example, take a distribution that is concentrated within 100 Hz for a
> center frequency, but has a -80 dB tail all the way out to 1 MHz away.
> The effective bandwidth is very wide in this case, but the signal is not
> likely to cause any interference to anybody.
>
>
>> From an English language point of view, the fact that you admit that the
>> "effective" bandwidth does increase with speed (even if not "by much"),
>> then it appears to me that you must also say that the sending speed is a
>> factor in determining the "effective" bandwidth of your J2A signal.
>
> The energy distribution under the spectral envelope changes and that will
> affect any "effective bandwidth". However, outside of the envelope all
> keying sidebands are attenuated by the spectral envelope.
>
> Basically, keying sidebands of a 20 wpm signal falls off at a faster rate
> than keying sidebands of a 10 wpm signal. I.e., the 10th keying sideband
> of a 20 wpm signal has as much energy as the 20th keying sideband of a 10
> wpm signal.
>
> Alex VE3NEA (another DSP type) had looked at CW keying envelope in the
> same manner. If you subscribe to QEX, you will find his article ("CW
> Shaping in DSP Software") that looks at a couple of different windows
> (Hamming, Raised Cosine, Gaussian, Blackman-Harris, etc) in the May/June
> 2006 issue of the bimonthly.
>
> I will be glad to scan and email the article (just 5 pages) for you if
> you don't have QEX handy.
>
>> Turning to my examples now in my eham article in which I calculated the
>> 99.1% power bandwidth, do you disagree with any of my numerical results?
>
> No, you are **NOT** wrong.
>
> I think your calculations are perfectly sound -- however, the window
> function that you are using is not the right one to use and therefore not
> attenuating the keying sidebands.
>
> If I am not wrong, your window function is equivalent to a cosine
> function between -pi/2 and +pi/2 and zero elsewhere. What this is
> equivalent to in the time domain is a cosine from -infinity to +infinitym
> that is multiplied by a pulse between -pi/2 and +pi/2.
>
> I.e., your window is
>
> w(t) = cos(t).pulse(t)
>
> where pulse(t) is 1 between -pi/2 and +pi/2, and is 0 elsewhere.
>
> Again, using the convolution theorem, the spectrum W(s) is therefore
>
> W(s) = F(cos(t))*F(pulse(t))
>
> where F() is the Fourier transform and * is the convolution operator.
>
> F(cos(t)) is just the Dirac delta, which is very narrow (theoretically
> infinitesimally narrow), but it is convolved with F (pulse) which is a
> sin(x)/x function.
>
> The problem is that sin(x)/x falls very slowly (envelope decays as 1/ x)
> and therefore does not fall off fast enough to attenuate the keying
> sidebands enough, so your effective bandwidth is very wide.
>
> From the mathematical viewpoint, the problem comes from the fact that
> there is a slope discontinuity when the pulse starts and another slope
> discontinuity when the pulse ends (even though there is no discontinuity
> in the function itself).
>
> So, even though f(t) is continuous, f'(t) is not and that is allowing the
> spectrum of the prototype pule to assume a very wide spectral shape.
>
> A better function souls be a *raised* cosine -- i.e., 1 + cos(x) -- that
> is starts at -pi (instead of -pi/2) and stops at +pi (instead of +pi/2).
> I.e., the leading edge of the prototype pulse slowly rises (instead of
> abruptly rises) and slowly tapes of to the top of the pulse. Ditto the
> trailing edge.
>
> I.e., instead of the function you'd used
>
> w(t) = cos(t) for -pi/2 < t < +pi/2
>
> use instead:
>
> w(t) = ( 1 + cos(t) )/2 for -pi < t < pi.
>
> In fact VE3NEA in his article specifically showed the example of the
> "sine shaping" (that is what he calls it) that you have used to show how
> slowly the spectrum decays.
>
> I am surprised that out of all those exchanges on eHam, no one had picked
> up this point! It is not your calculation that is wrong -- it is the
> fact that the prototype pulse that you had used to base the calculations
> on is not one that limits keying sidebands properly.
>
> I am sure that if you apply this second window function (raised cosine),
> everything will come out as the practical guys have measured on their
> spectrum analyzers. (a simple RC filter produces no slope discontinuity
> when a pulse is passed through the filter!)
>
> If you'd use a Blackman window, the far out spectrum would be even better
> than the raised cosine. But give the raised cosine above a shot first.
> I think it will prove my "slope discontinuity" point.
>
> Vy 73
>
> Chen, W7AY
 
RE: Bandwidth versus Keying Speed  
by W8XR on June 1, 2007 Mail this to a friend!
Mickey,

Thanks for posting the Chen exchanges.

His "raised cosine" window is what I was trying to get at in my examples.

My amateur suggestion was that the peaks and troughs of the raised sine function could be "stretched" to provide a quiet keying waveform - one that was not dependent on the keying rate (up to the risetime/falltime limits.)

But, I had not considered using some other windowing function for the keying shape - I figured Gaussian was probably "good enough". Some of these should provide even better keying characteristics.

Mark
 
RE: Bandwidth versus Keying Speed  
by AB0WR on June 1, 2007 Mail this to a friend!
w8ji:"Secondly, I reduced the speed to 4dps. That's pretty darned slow. The Occupied BW is 465 Hz. That's right in line with all the other measurements."

I would appreciate if you would copy the display and put it on your web site with the 10,25, and 40hz keying signals. I would like to see exactly what it shows at 4dps.

It shouldn't matter if this exercise is being done at 3.5Mhz or at 10khz. The mathematics for the modulation process is the same regardless of the carrier frequency. When I get time during summer break I am going to hook up my signal and function generators through an FET gate (i.e. one passing a 10khz sine wave that is biased on and off with a square wave) and see what the sound card shows for the spectrum at different keying rates using Cool Edit Pro. I can then add in RC low pass filters to limit the bandwidth of the square wave and see what that does to the output spectrum. We'll see if that matches what your spectrum analyzer shows. If it does, why then I'll have to take another look at the math. If it doesn't then we'll have to figure out exactly what the transmitters are doing that causes the system transfer function be different.

w8ji:"We can probably all look forever, but what Chen posted agrees with Kevin W9CF and many other people. Chen explains it well. Like W9CF, the measured data I get looks exactly like the predictions of W9CF and many other people."

What he posted agrees with a system whose InputFunction bandwidth is wider than the SystemResponseFunction which causes the OutputResponsefunction to look like the SystemResponseFunction. If you hang a big picture outside your house over a small windowpane all you can see of the picture is what the windowpane covers. If you then hang a small picture outside your house over the window pane, especially one that is smaller than the window pane, then you can see the entire picture.

If you start out with a small picture, i.e. a 4hz keying waveform, and it gets converted to a *big* picture by hanging it outside your house (i.e. a 500hz bandwidth), then either the hanging process or the window pane is *doing something* other than just being a window pane (i.e. an RC low-pass filter function). It is somehow affecting the input signal to make it different.

The square wave function depends on a 1/x amplitude relationship between the fundamental and the odd-order higher harmonics in order to retain the proper relationship and make the bandwidth what is calculated. If the system response is non-linear, i.e. the amplitude of the fundamental is being compressed (because a stage in the transmitter is being run into saturation) so that the amplitude relationship between the fundamental and the harmonics is changed from the input then all bets are off.

That is one possible explanation of why the bandwidth of a pulse train is not what is expected. But that still doesn't make the statement that the slope of the output wave generates the harmonics causing the bandwidth. The rise time is *STILL* an indicator of a limited bandwidth system response, nothing more. In essence, there would be two system response components that would have to be accounted for. In fact, what would be happening from a non-linear stage saturating on the fundamental would be a whole set of intermod products from the mixing of all of the harmonics of the input square wave. The result of that would be very complex to study but it would account for both the extended bandwidth as well as key clicks far removed from the fundamental carrier frequency.

I know that my old Globe Chief 90a also suffered from big power supply dropoff during a long CW pulse. In essence, it was like laying an exponential decay function on top of the system response. That alone would cause the system gain response to become non-linear thus generating all kinds of intermod products which would, in turn, make the OutputResponse function look much wider than it should.

Does anyone else have any ideas on what else would cause a transmitter to change the bandwidth of a 4hz input square wave to a 500hz power bandwidth?

The math that Mickey has used is correct. If it isn't then there any number of electrical, civil, mechanical, industrial engineers, and even biologists, all of whom use Fourier series and transforms to study various phenomena, including biological phenomena, who are alive today who need to be told that their all their knowledge and research needs to thrown in the dumpster because W8JI and W9CF say that the slope of a square wave generates harmonics rather then indicating a bandwidth limited system response to an input function.

I don't think that is going to happen. Therefore, it would behoove us to figure out why the 751a transmitter Tom is measuring has a system response function that causes the input bandwidth to be extended.

BTW, Tom, how do you hear key clicks out beyond 500hz from a system that is bandwidth limited to 500hz? Or are you saying that the bandwidth * rise-time = pi is also wrong for a square wave response?

tim ab0wr

tim ab0wr
 
RE: Bandwidth versus Keying Speed  
by W8XR on June 1, 2007 Mail this to a friend!
I respectfully disagree with your assertion regarding rise time. The keying waveform isn't an indicator of limited bandwidth system response - it's merely the shape of the keying waveform in use. The steeper the leading and trailing edges of the keying waveform, the more high frequency harmonic components it contains. The more harmonics are mixed with the carrier to produce a wide bandwidth signal.

The use of any poorly formed keying waveform (one with steep sides or discontinuities) will result in a wide bandwidth signal. The use of a well formed keying waveform (one with slowly sloping sides and no discontinuities or abrupt transitions) will result in a narrower bandwidth signal.

I think Chen made this point rather well.
 
RE: Bandwidth versus Keying Speed  
by W8XR on June 1, 2007 Mail this to a friend!
I hit send before the final edit... the second sentence has been edited, below.

I respectfully disagree with your assertion regarding rise time. The [rise time of the] keying waveform isn't an indicator of limited bandwidth system response - it's merely the shape of the keying waveform in use. The steeper the leading and trailing edges of the keying waveform, the more high frequency harmonic components it contains. The more harmonics are mixed with the carrier to produce a wide bandwidth signal.

The use of any poorly formed keying waveform (one with steep sides or discontinuities) will result in a wide bandwidth signal. The use of a well formed keying waveform (one with slowly sloping sides and no discontinuities or abrupt transitions) will result in a narrower bandwidth signal.

I think Chen made this point rather well.
 
RE: Bandwidth versus Keying Speed  
by W9AC on June 1, 2007 Mail this to a friend!
AB0WR: "If you two would actually read what is being posted this is what you would find..."

Tim, please read Chen's analysis and get back to us.

Regards,

Paul, W9AC
 
RE: Bandwidth versus Keying Speed  
by KE3HO on June 1, 2007 Mail this to a friend!
I think that it is interesting that Tom and Mickey both posted letters from Mr. Chen. It would appear that both Tom and Mickey hold Mr. Chen in high esteem and value his opinion.

Reading Mr. Chen’s letter to Tom, it seems to say that Tom is correct – the bandwidth of a CW signal is dominated by the shape of the leading and falling edges of the keying waveform, not by the pulse width (or keying speed).

Reading Mr. Chen’s letter to Mickey, it seems to say that Mickey’s *calculations* are correct, but that the difference between his calculated bandwidths and Tom’s measurements are due to Mickey’s choice of his window function, and that if he had used a raised cosine for his window function that his calculated bandwidths would agree more closely with Tom’s measurements.

The bottom line, IMHO, is that Mickey’s calculations are mathematically correct, but that the window function that he chose does not match the type of keying waveform found in typical transmitters, and that substitution of a different window function would give results matching real world measurements. If a transmitter were made with a keying function that matched Mickey’s window function, the transmitter would almost certainly perform just as Mickey has calculated.

You are all, of course, free to draw your own conclusions. You are also free to jump in here to comment on my above statements. However, rather than having a bunch of people on one side jump in here and say that I am right, and a bunch of people on the other side jump in and say that I am full of fertilizer, I would love for someone to ask Mr. Chen if my summary is correct. (Mr. Chen must feel like he just stepped in between the Hatfields and the McCoys)

73 - Jim
 
RE: Bandwidth versus Keying Speed  
by WR8Y on June 1, 2007 Mail this to a friend!
wr8y:"Did you read the rest of my post? I then resorted to using the 170 hz filter in the 830 while listing to a stream of dits - adjusting the speed from 5 WPM to 40 WPM. NO BANDWIDTH CHANGE!"

Exactly what did you expect to hear that would indicate a change in bandwidth?

Did you expect the sound you heard to change from a tone to a buzz if the bandwidth changed?

If what you heard didn't change, exactly how does that relate to the bandwidth not changing?

I would be very interested in knowing exactly what you would expect a change in bandwidth to "sound" like? Can you define what the different bandwidths would sound like if they, in fact, *did* change?
------------------

Where the hell did I say I "heard" anything? I OBSERVED no change in bandwidth by sweeping across the transmitted signal with the '830's receiver. (Using narrow filter and tightening down the passband to ~170 hertz. It's not hard to do.
 
RE: Bandwidth versus Keying Speed  
by WR8Y on June 1, 2007 Mail this to a friend!
OOPS. I did say "heard" - not a good choice of words. I can see how you read into my statement what you did!

What I did was what ANY HAM HERE CAN DO, I listened to a varying speed of dits from one transmitter on another receiver with a tight filter, sweeeping across the transmitted signal.

Using a stream of dits sent adjusted to 5 WPM, then a stream of dits at 40 WPM, I saw no change in bandwidth.

And I must say, I have never noticed that highspeed CW has any wider bandwidth than a novice at 5 wpm.

Anyone who has studied electronics in school has been required to do MORE than read a book and punch buttons on a calculator - time to do a lab demonstration, guys!

SHOW me your theory in a lab experiment.
 
RE: Bandwidth versus Keying Speed  
by AD5X on June 1, 2007 Mail this to a friend!
W8RY: "SHOW me your theory in a lab experiment."

Bravo - This is what we always do in the real product development world. And this will validate your (K5MC) model. We've seen experiments run by W8JI and W8RY that indicate your model is not correct. I'm not talking about the math - I'm talking about the model that the math is applied to. Rather than criticize the measuremtns done, run your own experiments on real transmitters and show us. I just made some very simple measurements of my own. I transmitted with my IC-706MKIIG into a dummy load, and then looked at the signal with my Yaesu MKV using a 60HZ DSP filter (basically using the MKV as a selective level meter). The MKV has a shorted input RF connector (shorted through a relay) and also has 18dB of front end attenuation in-line which gives me an S9 reading on the S-meter when tuned exactly to the IC-706 frequency. Tuning the MKV in 50HZ increments, I wrote down the S-meter reading (looking at the peak-hold bar) using 6WPM and 30WPM. I ran these tests a bunch of times. I could not really see any difference, other than at -250Hz (data below):

IC-706G frequency = 21.030.000

Freq. 30WPM 6WPM
0 S9 S9
-50Hz S9 S9
-100Hz S8 S8
-150Hz S7 S7
-200Hz S5 S5
-250Hz S3 S2
-300Hz S0 S0

Of course, I have no idea how accurate the S-meter readings are, and eyeballing the bargraph S-meter on the MKV isn't the best thing in the world. But this relative test does indicate that BW does not vary with keying speed.

Phil - AD5X
 
RE: Bandwidth versus Keying Speed  
by AB0WR on June 1, 2007 Mail this to a friend!

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
w8xr:" respectfully disagree with your assertion regarding rise time. The keying waveform isn't an indicator of limited bandwidth system response - it's merely the shape of the keying waveform in use. "
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

I'm sorry, this just can't be. The keying waveform starts at your cw key. It is just a switch. It is either on or off. The keying waveform begins as a pure square wave (disregarding contact bounce and contact resistance). It just doesn't get any more square than this.

This square wave waveform goes into the black box that is your transmitter. That black box takes that square wave input, does what ever it does to the square wave, and provides an output response.

That black box has a system response function. Call it G(w), H(w), S(w) or whatever. I've seen it called a lot of different things in a lot of different places.

That system response function, coupled with the input signal, is what determines the output response. If that output response is a quare wave with a non-zero rise time then you know that the system response function does NOT provide an infinite bandwidth. The amount of the rise time will tell you the system response bandwidth.

Even in a DSP system where the output function is generated directly you will find the math derived from the very same roots. You start with a square wave with an infinite number of harmonics and then you apply a bandwidth-limited response function (it can be a simple loww-pass filter, a gaussian filter, a raised cosine filter, or whatever) to diddle with the harmonics to get the output response you want.

This is elementary. I gave you three web sites to go look at that explains this in detail. It isn't just something that I made up. From the Tektronics site to the Wikipedia site, they all say the same thing.


<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
w8xr:"The steeper the leading and trailing edges of the keying waveform, the more high frequency harmonic components it contains. The more harmonics are mixed with the carrier to produce a wide bandwidth signal. "
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

That keying waveform starts out as a square wave with an infinite number of harmonics (they may be impossible to measure in the higher numbered ones but they exist nonetheless). Unless the CW key you use is different than any key I have ever seen it is just an on-off switch. There is no shaping done by any key that I know of.

I do agree that the more harmonics the system will transmit the wider the bandwidth you will see. The smaller the rise time the higher the number of harmonics being sent. If, however, the input waveform has a smaller bandwidth than the system response bandwidth you will see the input response repeated in the output response with no degradation (assuming linear amps and all that). If the input waveform has a wider bandwidth than the system response then the output response will be a degraded copy of the input waveform.

w8xr:"The use of any poorly formed keying waveform (one with steep sides or discontinuities) will result in a wide bandwidth signal."

I have no disagreement with this.



w8xr:" The use of a well formed keying waveform (one with slowly sloping sides and no discontinuities or abrupt transitions) will result in a narrower bandwidth signal. "

And I have no disagreement with this.


w8xr:"I think Chen made this point rather well. "

We disagree on what his point is. The way I read it his point assumes an input waveform with a wider bandwidth (i.e. a comb function) than the system response bandwidth. Of course this will result in a shaped output response and the shaping will look exactly like the system response window in the frequency domain. It simply does not address the issue, however, of what happens when an input waveform has a *smaller* bandwidth than the system response function. An input waveform with a power bandwidth of 42hz should pass through a system with a system response bandwidth of 500hz with no change. The system response will *not* somehow magically stretch the input bandwidth to 500hz as long as it is only a bandwidth limiting response function. It's like running a chunk of 10 gauge copper through a 12 guage die. Copper is removed until its size is 12 guage. Look at the system response as that wire die and the copper wire as the input waveform. That input waveform will get stripped down to be no wider than the bandwidth of the system response function. On the other hand, if you run a 14ga wire through that 12 gauge die nothing happens to the wire. Thats just like running a 42hz bandwidth signal into a system with a 500hz bandwidth response. The 14ga wire doesn't get ballooned out to 12ga and the 42hz bandwidth shouldn't get ballooned out to 500hz.

The shah function that was mentioned by Chen is nothing more than an infinite train of impulses spaced at intervals of T. In other words, it is a VERY HIGH BANDWIDTH signal, effectively infinite in bandwidth. It is defined as the sum from negative infinity to positive infinity of e^jwt. You don't get any wider than this. Unless you have an infinite system response function, this input waveform is going to get modified in some manner. And that is all Chen is saying. It simply doesn't address the case of what happens when the input waveform has a smaller bandwidth than the system response function.

If you don't believe me, go look at the web sites I quoted. They explain exactly the same thing in exactly the same way. If you don't understand your inputs and you don't know what your system response is then there is little you can do to determine the system output response.

If Tom is correct that a 42hz bandwidth signal waveform, when input into a 751a transmitter, comes out as a 500hz bandwidth signal then something is going on in that 751a that is much, much more than a bandwidth-limiting system response function. It will be fun to find out exactly what that is. I can guarantee you that it is NOT the rise time of the output response that is "generating" bandwidth. Outputs waveforms don't generate anything. Inputs waveforms and system response functions *generate* output waveforms, not vice-versa.

tim ab0wr
 
RE: Bandwidth versus Keying Speed  
by AB0WR on June 1, 2007 Mail this to a friend!
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
w9ac:
AB0WR: "If you two would actually read what is being posted this is what you would find..."

Tim, please read Chen's analysis and get back to us.

Regards,

Paul, W9AC
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Paul, I did read it, did you?

Do you know what a shah function is?

It is an infinite bandwidth signal. Of course an infinite bandwidth input waveform, when submitted to a system response function with a limited bandwidth response, is going to assume the shape of the system response function in the frequency domain.

Did you expect anything else?

This is nothing more than the elementary Fourier equation that the OutputResponse(w) = Input(w) x SystemResponse(w).

This still does not explain how an input signal that is *narrower* in bandwidth than the system response function gets stretched to almost 10 times the bandwidth in the output function. Something like a 400hz RC lowpass filter in the keying circuit to generate a bandwidth limited response function is NOT going to stretch an input signal with a 42hz power bandwidth out to an output response with a power bandwidth of more than 400hz.

If you can explain how a simple lowpass filter can acommplish this using the appropriate mathematics I would dearly *LOVE* to see it.

As Chen pointed out, Mickey's calculation of power bandwidths are correct for a bandwidth limited square wave. That means that a 1hz keying speed with a 5ms rise time has about a 42hz power bandwidth. I fail to see how that magically gets converted into a 500hz bandwidth in the output of a 751a transmitter unless that transmitter has more than a simple bandwidth-limiting system response function.

I have yet to see anyone show that Mickey's calculations are incorrect. If Tom's measurements are correct then *SOMETHING* more than a bandwidth-limited system response *HAS* to be in play. I have yet to see anyone explain what this is.

Saying that the slope of the output square wave "generates" harmonics is just plain incorrect. That slope is the *result* of a bandwidth limited system limiting the harmonics being passed, it is not the generator of harmonics.

I believe the 751a generates CW by keying a LO signal does it not? Then that keyed LO signal is mixed with the VFO signal to generate the actual output response, right? If that is true then I have no idea what all could be happening in any pre-mixer amplifiers, the mixer itself, any post-mixer amplifiers, the driver circuity, or the final amp itself. It is entirely feasible that a stage along the way is being driven into saturation thus generating all kinds of intermod products close in to the CW signal itself making the signal look much wider than it actually should be. In other words, the system response function may not be a simple bandwidth-limited response.

Instead of considering such possibilities you and Tom seem to want to insist that the math learned by all kinds of engineers, not just electrical engineers, has been wrong for more than 100 years.

You simply cannot look at the output of a black box and say that it invalidates all kinds of known physics without knowing in detail the input to the black box and the system response of the black box. Mickey has tried to explain the significance of the input signal. What is left is to characterize what is happening in the system response function.

You and Tom can ignore this process if you will and just continue to tell us that the simple math of square waves has to be wrong. If you do, however, you are just going to get left in the dust as the rest of us figure out what is going on.

tim ab0wr
 
RE: Bandwidth versus Keying Speed  
by W8XR on June 1, 2007 Mail this to a friend!
I'm sorry, I misunderstood your use of the word "system".

I don't use a key, I use a software keyer that generates the keying waveform and I/Q signals that are then upconverted to RF. So for me "system" starts with two inputs: 1.) Keying Envelope and 2.) carrier. (As it turns out these are merely blackbox constructs - in the SDR environment this is all in software so there really isn't a keying envelope or carrier. But I still use these abstractions for discussion.)

My apologies for missing your point.

My point was that if you modulate a carrier with a well shaped keying envelope it doesn't matter how fast you transmit (within the limits of the rise/fall time of the envelope.) Hence, my assertion that the bandwidth of the output is constrained by the rise/fall of the keying envelope and not the sending speed (at least for a 5ms rise/fall and otherwise monotonous envelope at typical amateur speeds - up to about 200+ WPM where the rise/fall no longer provide adequate pulse length.)

Again, sorry for misinterpreting "system".

Mark
W8XR
 
RE: Bandwidth versus Keying Speed  
by AB0WR on June 1, 2007 Mail this to a friend!
ke3ho:"The bottom line, IMHO, is that Mickey’s calculations are mathematically correct, but that the window function that he chose does not match the type of keying waveform found in typical transmitters, and that substitution of a different window function would give results matching real world measurements. If a transmitter were made with a keying function that matched Mickey’s window function, the transmitter would almost certainly perform just as Mickey has calculated. "

Jim,

This is from my Signals, Systems, and Communications textbook by B.P. Lathi, copyright 1965.

"Consider a system with the transfer function H(s). If r(t) is the response of the system to a driving function f(t) and if R(s) and F(s) are their respective transforms, then

R(s) = F(s)H(s) equation (10.1)"

The keying function, i.e. the "window" function, is the response of the system mentioned in the quote above, it is H(s). The driving function, f(t) is the square wave input from the CW key. The output of a CW key *has* to be a square wave, it can only be on or off.

The window functions Chen, as well as the rest of us, have been discussing are frequency response functions (i.e. H(s)) not frequency generation functions. Therefore they can only modifiy the input function. The "window" functions can't "generate" anything of their own.

I wish I could draw a picture of this but it really *is* like looking at a picture through a pane of glass with everything outside the pane covered up. You can have round panes, cosine shaped panes, raised cosine shaped panes, gaussian shaped panes, big panes, small panes, etc. Each will let you see different sizes and shapes of the picture (i.e. different bandwidths) but none can extend the picture beyond what is already there (i.e. the input "driving" function). If the picture is smaller than the pane then you can see it all, the input signal gets through with no bandwidth modification. If the picture is larger than the pane then you only get to see part of it, the bandwidth of the input signal is cut down to match that of the response function.

In order to change the power bandwidth of a square wave with a 5ms rise time from 42 hz to more than 400hz (a whole order of magnitude change), something more than a window function would be required inside that black box we know as a transmitter.

Professor Lathi goes on to say:

"The principles of frequency analysis of linear systems may be expressed succintly as follows:

1) the response of a linear time-invariant system to an external exponential signal e^st is given by H(s)e^st.

e^st <-> H(s)e^st

2. By means of frequency transforms, every driving function f(t) can be expressed as a continuous sum of exponential functions.

f(t) = (1/j2pi) Integral F(s)e^st ds

with integration limits of sigma + j(infinity) and sigma-j(infinity).

3, By the virtue of linearity, the principle of superposition applies, and the response r(t) is given by a continuous sum of the responses of the system to individual components.

r(t) = (1/j2pi) Integral H(s)F(s)e^stds"

Mickey has done No. 2. He has broken down the square wave driving function into its components. He has also attempted to accomplish No. 1 by defining the system response, H(s), as a bandwidth limiting response, i.e. a shaped square wave with a given rise time (think bandwidth = pi/rise-time for a square wave).

He has used these to calculate No. 3. W8JI and W9CF are trying to imply that these calculations must be wrong because they don't describe what they see. But the calculations *are* correct. There just isn't any question about it.

That means that Step No. 1 is the area that needs to be looked at. The system response function H(s) *must* be something other than a frequency response window function in most transmitters. It *has* to be if it is actually *generating* frequency components.

Tom and Paul would be better off trying to help explain what that system response function has to be rather than in continuing to say that all the math has to be wrong. Who knows, we might come up with a major modification for the 751a that will make it an even better CW rig!

We better hope that we can come up with something else or no CW will be allowed in the ARRL 200hz bandwidth segmentation areas. If the necessary bandwidth of a CW signal is 500hz, those really narrow areas will be reserved only for psk31, psk125, etc. Please also note that if the claim is made that the *real* necessary bandwidth for CW is actually less than 500hz then that is a tacit admission that something besides a frequency response window is going on inside the transmitter that is extending the necessary bandwidth to make it wider than needed.

tim abw0r

 
RE: Bandwidth versus Keying Speed  
by W8JI on June 1, 2007 Mail this to a friend!
Tim,

You might as well give up on blaming the 751A. A Viking Valiant and a Globe Scout 65 and even a DX 60 act the same way. So does my two tube cathode keyed 6AG5 driving an 807. My Yaesu's and Ten Tec's do the same.


You made this statement:

"In order to change the power bandwidth of a square wave with a 5ms rise time from 42 hz to more than 400hz (a whole order of magnitude change), something more than a window function would be required inside that black box we know as a transmitter."

Where did that 42Hz come from? I can't find it.

73 Tom



 
RE: Bandwidth versus Keying Speed  
by W9AC on June 1, 2007 Mail this to a friend!
AB0WR: "I have yet to see anyone show that Mickey's calculations are incorrect. If Tom's measurements are correct then *SOMETHING* more than a bandwidth-limited system response *HAS* to be in play. I have yet to see anyone explain what this is..."

Tim, I don't believe anyone is refuting K5MC's calculations -- what is being questioned is whether or not the correct theorem is being applied to a problem. See Chen's comments on this.

This from K5MC:

"I believe that W8JI is simply being mislead by his analyzer!"

That's a pretty strong statement. We're led to believe that measured data cannot possibly trump the mis-application of a theorem.

Let's start by proving that the claimed theorem is the right tool for the analytical application and that the analytical theorem offered by W9CF is in incorrect. Proof, please.

The reasonable explanation is that the spectrum analyzer is not the root-cause of the discrepancy. Rather, the analytical tool is not the right one for job. Tim, what is it about the SA samples you disagree with? The Res BW? The sweep time? Where do you want it?

> "BTW, Tom, how do you hear key clicks out beyond 500hz from a system that is bandwidth limited to 500hz? Or are you saying that the bandwidth * rise-time = pi is also wrong for a square wave response?"

This suggests a lack of understanding of the issue. Aside from a S/A, one can easily use a receiver and tune to either the side of a keyed, transmitted carrier and hear key clicks with any filter setting. If key clicks are generated 5 kHz from the carrier F, the ability to tune the Rx VFO into the upper transmitted spectrum is all that is necessary, even with a narrow filter. We can use a 250 Hz filter, a 2.8 kHz filter, or even a 6 kHz filter to detect the presence of key clicks -- it's done by moving the receiver's VFO to put the clicks into the receiver's filtered passband.

If I am using a 250 Hz filter and I hear clicks at 7.010 MHz and the interfering station is on 7.005 MHz, I'ved just proved that the clicks are present well beyond the limits of the filter's passband.

> "Does anyone else have any ideas on what else would cause a transmitter to change the bandwidth of a 4hz input square wave to a 500hz power bandwidth?"

Yes, it's the rise and decay function of the keyed waveform as we've been discussing all along -- and analyzed/documented by W9CF.

> "Professor Lathi goes on to say:.."

I have nothing but respect for Lathi, but can we leave the Wikipedia "copy and paste" out of this?

Regards,

Paul, W9AC
 
RE: Bandwidth versus Keying Speed  
by AB0WR on June 1, 2007 Mail this to a friend!
w8xr:"My point was that if you modulate a carrier with a well shaped keying envelope it doesn't matter how fast you transmit (within the limits of the rise/fall time of the envelope.) Hence, my assertion that the bandwidth of the output is constrained by the rise/fall of the keying envelope and not the sending speed (at least for a 5ms rise/fall and otherwise monotonous envelope at typical amateur speeds - up to about 200+ WPM where the rise/fall no longer provide adequate pulse length.) "

Using a well-shaped keying envelope *will* limit the transmitted bandwidth. There just isn't any doubt about that.

And the *maximum* bandwidth of the output *is* constrained by the bandwidth of the system response function. That doesn't specify the minimum bandwidth of the system, however.

Look at it this way - an RC low pass filter with a cutoff of 600 hz would eliminate all of the harmonics of a 100hz square wave that are above 600hz. The 3rd harmonic would be at 300hz, the 5th harmonic would be at 500hz, and the 7th harmonic would be at 700hz. So you would wind up with a square wave consisting of only the fundamental and the 3rd and 5th harmonics. It's not going to look like a very good square wave.

If you apply a 5hz signal to that same filter, you will get odd harmonics all the way out to the 119th. A much better square wave will result.

If we assume that the harmonics tend to start getting unmeasurable around the 30th harmonic (if I remember this correctly, I could be off on this), the absolute bandwidth of the 5hz square wave would be 150hz compared to the absolute 500hz of the 100hz square wave. Thus you would have less interference to adjacent channels even though you might be sending a square wave with shorter rise times.

If your software defined radio has the same shape keying envelope, in the time domain I assume?, no matter what speed you send or what length of element you send then I would tell you that the radio is changing the filter reaponse to match your keying speed. If this is true, the actual bandwidths you send should change as you change keying speeds, the shouldn't stay constant.

This whole idea that the bandwidth of square waves is constant just floors me. If that were true the telephone companies could use T1 carrier (1.544Mhz) cable to send T2 carrier (6Mhz) signals since the square waves being used would have exactly the same bandwidth. This is exactly the same logic as saying a 4hz square wave results in exactly the same bandwidth as a 40hz square wave (an order of magnitude difference). And yet I know that T2 cable required a much higher cutoff bandwidth and needed special low-capacitance cable to provide this. T1 cable simply wasn't capable of carrying the T2 spectrum. That's a dead giveaway to me that square waves of different frequencies don't have the same bandwidth.

tim ab0wr



 
RE: Bandwidth versus Keying Speed  
by AB0WR on June 1, 2007 Mail this to a friend!
"Where did that 42Hz come from? I can't find it. "

Look at the original message. It's a 2.4wpm, 1hz square wave power bandwidth.

If the power bandwidth of a square wave, that's a waveform with the maximum number of harmonics and zero rise time, is 42hz but the power bandwidth becomes *higher* when the wave is bandwidth limited, i.e. a rise time is appears on the wave, then the whole world is upside down. That means we could generate higher and higher bandwidths by using longer and longer rise times.

Either the power bandwidth is maximum when the rise time is zero or the power bandwidth is maximum when the rise time is NOT zero. It can't be both.

You and Paul seem to be trying to convince us that the power bandwidth is NOT maximum when the rise time is zero. That somehow the power bandwidth goes up when the rise time gets longer.

Now I suppose it could be that Mickey's calculations of power bandwidth for a square wave are wrong but I've yet to see anyone show just where. In fact, I have yet to see anyone actually say that they are wrong.

So that leaves us with the connundrum of how does the bandwidth of a square wave go up when the rise times get longer?

And please don't use the canard that the slope of the rise time generates the bandwidth. It doesn't, at least not if the response function of the system is a frequency domain filter window. Filter window response functions don't generate anything, they only modify inputs. And even the slope of a filter response function did generate harmonics that means that shorter rise times would give wider bandwidths which, in the limit, would mean that a zero rise time would give the widest bandwidth. But that is what you are saying is NOT happening since you are saying that a rise time on a 1hz CW signal will give a 500hz power bandwidth even when a perfect 1hz square wave has a 42hz power bandwidth. It's a form of argumentative fallacy called begging the question - i.e. using the conclusion as your premise. It's a vicious circle which provides no real answer.

tim ab0wr

 
RE: Bandwidth versus Keying Speed  
by KE3HO on June 1, 2007 Mail this to a friend!
Tim,

I think that you are misinterpreting Chen’s comments. Also, with regards to the keying waveform, you are considering the open/close of the key as the keying waveform. That open/close is shaped by the rig to give it a smooth rising and falling wave shape. That shaped waveform is the keying waveform and is the input to the system.

When I read Chen’s analysis, I see the following. The keying waveform, which is the modulation to the RF stage, he describes as a square (or rectangular wave) that is convolved with a wave-shaping window function. The square/rectangular wave sets the overall pulse width while the convolution with the wave-shaping window function sculpts the rising and falling shape of the keying function. The convolution in the time domain is, as Chen points out, a simple multiplication in the frequency domain after the FT is taking of the square/rectangular wave and the wave-shaping window function.

In Chen’s own words:

“Notice that for any smooth function that you use as a window, it's Fourier transform will fall faster than the envelope of the sin(x)/s function -- i.e., for a reasonable wave-shaping, the Fourier transform of the Gaussian falls off faster than 1/f where f is frequency.

Ergo, it is the wave-shaping function that is what governs the bandwidth of the shaped pulse, it is not the pulse width.”

That seems pretty clear to me. It is the shape of the rising and falling edge of the keying waveform that dominates the bandwidth, not the pulse width.

Then Chen goes on to discuss what happens when you have a train of pulses rather than a single pulse. He describes the keying waveform as a comb function convolved with the prototype keying function he described above.

Once again, in Chen’s own words:

“Again, from the Fourier Duality statement, the spectrum of a series of dits is just a product of the Fourier transform of the prototype shaped pulse and a comb in the frequency domain. Again, the spectrum of the window predominates and knocks out all the higher frequency components of the comb.”


That also seems pretty clear to me. The shape of the rising and falling edges of the keying function dominates the bandwidth for a series of dits, not the width of the pulses.


Now, what did Chen have to say about Mickey’s calculations?

Chen: “I think your calculations are perfectly sound -- however, the window function that you are using is not the right one to use and therefore not attenuating the keying sidebands.”

Chen: “The problem is that sin(x)/x falls very slowly (envelope decays as 1/x) and therefore does not fall off fast enough to attenuate the keying sidebands enough, so your effective bandwidth is very wide.

From the mathematical viewpoint, the problem comes from the fact that there is a slope discontinuity when the pulse starts and another slope discontinuity when the pulse ends (even though there is no discontinuity in the function itself).

So, even though f(t) is continuous, f'(t) is not and that is allowing the spectrum of the prototype pulse to assume a very wide spectral shape.

I am sure that if you apply this second window function (raised cosine), everything will come out as the practical guys have measured on their spectrum analyzers.”

That too is pretty clear: Mickey’s calculations are *mathematically correct* - in other words, he did not make an error in calculation. However, Chen states very clearly that the problem is Mickey’s choice of his window function, which has a slope discontinuity, and it is this slope discontinuity that causes the prototype pulse to “assume a very wide spectral shape”. And finally, Chen is very clear that if Mickey were to use a more suitable window function, he is sure that the calculations will agree with the spectrum analyzer plots.

Personally, I think that Mickey did an excellent job in his analysis and in presenting the information here. I think that there was a fundamental flaw in the underlying assumptions that the analysis was based on, and Mr. Chen pointed out what that flaw was – the choice of window function. My conclusion from Mr. Chen’s comments: if Mickey had chosen a more suitable window function (i.e. a window function that more closely represents the leading and trailing wave-shaping of a typical CW transmitter) his calculations would agree with Tom’s measurements on the spectrum analyzer.

I am not attacking Mickey here. I have tremendous respect for Mickey, and I commend him on the work that he did in his analysis. I certainly would not have discovered the source of disagreement between his calculations and Tom’s measurements, and only through reading Mr. Chen’s comments do I finally understand where the difference comes from.

Mickey - have I unfairly summarized Chen's comments, or have I misunderstood them?

73 - Jim
 
RE: Bandwidth versus Keying Speed  
by AB0WR on June 1, 2007 Mail this to a friend!

w9ac:"Tim, I don't believe anyone is refuting K5MC's calculations -- what is being

questioned is whether or not the correct theorem is being applied to a problem. See

Chen's comments on this. "

I have seen Chen's comments on this. I explained them to you. I have yet to see you

refute my explanation. Again, a shah function is an infinite bandwidth function. Do

you really expect this to result in anything except a shaped response when a filter

window is applied to it?

Do you expect a input driving function to EXPAND its bandwidth when it is also applied

to the same filter window? If so, please provide the math to show how this happens

since it violates all of the convolution rules for both the time domain and frequency

domain that I learned.


<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
This from K5MC:

"I believe that W8JI is simply being mislead by his analyzer!"

That's a pretty strong statement. We're led to believe that measured data cannot

possibly trump the mis-application of a theorem.

Let's start by proving that the claimed theorem is the right tool for the analytical

application and that the analytical theorem offered by W9CF is in incorrect. Proof,

please.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>


You have been provided the proof in at least three messages now. You have yet to

respond to any of them. You just keep asking for proof over and over. You consider

this a valid discussion method?

Again, this is a fundamental theorem:

R(s) = F(s)H(s)

where R(s) is the transform of the output response, F(s) is the transform of the

driving response (i.e the input), and H(s) is the transform of the system response

function.

Question 1: Do you agree with this fundamental theorem?



The transmitter *IS* a system. Therefore it has a system response function. Our

analytical model assumes this system has a linear response and it is described by a

bandwidth limiting function since a perfect square wave input results in an output

response that is bandwidth limited, i.e. a square wave with a rise time.

Question 2: Do you agree with this assumption?

Question 3: If you do not agree then how would you characterize the system response

function for the black box that is a transmitter.


<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
The reasonable explanation is that the spectrum analyzer is not the root-cause of the

discrepancy. Rather, the analytical tool is not the right one for job. Tim, what is it

about the SA samples you disagree with? The Res BW? The sweep time? Where do you want

it?
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Did you think my call is K5MC for some reason?



<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
> "BTW, Tom, how do you hear key clicks out beyond 500hz from a system that is

bandwidth limited to 500hz? Or are you saying that the bandwidth * rise-time = pi is

also wrong for a square wave response?"

This suggests a lack of understanding of the issue. Aside from a S/A, one can easily

use a receiver and tune to either the side of a keyed, transmitted carrier and hear

key clicks with any filter setting. If key clicks are generated 5 kHz from the carrier

F, the ability to tune the Rx VFO into the upper transmitted spectrum is all that is

necessary, even with a narrow filter. We can use a 250 Hz filter, a 2.8 kHz filter, or

even a 6 kHz filter to detect the presence of key clicks -- it's done by moving the

receiver's VFO to put the clicks into the receiver's filtered passband.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

If key clicks are generated 5khz away from a square wave with a 1hz frequency then you are hearing the 5000th harmonic. For a keying waveform with a 2hz frequency you would be hearing the 2500th harmonic. For a keying waveform of 4hz you would be hearing the 1250th harmonic. The 1250th harmonic would be something like -62db down from the fundamental.

Question 4. Just how strong of a signal are you putting out that you can hear the 1250th harmonic of a 4hz keying wave that is 62db down from the fundamental?

Question 5. If you can hear the 1250th harmonic of a 4hz keying wave how sure are you that you aren't nearing artifacts from an overloaded receiver?



<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
If I am using a 250 Hz filter and I hear clicks at 7.010 MHz and the interfering

station is on 7.005 MHz, I'ved just proved that the clicks are present well beyond the

limits of the filter's passband.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

The only thing I can say is -- So? You need to answer Questions 4 and 5 to further the discussion. I'll even add another question.

Question 6: How do you know that this key click that is 5000hz away, the 1250th harmonic of a 4hz keying wave is not being generated by intermod products somewhere in the transmitter chain? This is exactly what one would expect from a transmitter being driven into non-linearity somewhere. It is the exact same thing that one hears on SSB from someone over driving an amplifier and causing buckshot several kilohertz away from his operating frequency.



>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
> "Does anyone else have any ideas on what else would cause a transmitter to change

the bandwidth of a 4hz input square wave to a 500hz power bandwidth?"

Yes, it's the rise and decay function of the keyed waveform as we've been discussing

all along -- and analyzed/documented by W9CF.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Your analysis is doing nothing more than than calculating the bandwidth of an output response from a system. You calculate the bandwidth of an output response indicated by the rise time of that output response and then use it in a non-causual way to say that this output function will *always* be the output function no matter what the input driving function is or what the system response function is. You are analyzing an *OUTPUT* response and then are trying to say that it is both the input driving function as well as the system response function.

As I told Tom, this is called "begging the question". It is using the conclusion as a premise, i.e. the output will the output because it is the output.

You need to show in your analysis how the F(s) and H(s) terms result in your R(s) term. We know that the input to the system is a perfect square wave. A CW key cannot produce anything else. That leaves the H(s) system response function to be evaluated.
If we can't get from a 4hz square wave leaving the CW key on the desk to a 400hz output response then how will we ever be able to tell what is happening inside that black box we call a transmitter?


<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
> "Professor Lathi goes on to say:.."

I have nothing but respect for Lathi, but can we leave the Wikipedia "copy and paste"

out of this?
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

No, we can't. He is an accepted authority whereas I am not. When what he says confirms what I am saying, I will continue to use him as an authority. I'm sorry if that offends you but it's just the way it will be.

Now, can you answer the questions above?

Or are you going to continue to ignore them?

tim ab0wr
 
RE: Bandwidth versus Keying Speed  
by AB0WR on June 2, 2007 Mail this to a friend!
ke3ho: "think that you are misinterpreting Chen’s comments."

That's always possible but I haven't seen it yet.

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
Also, with regards to the keying waveform, you are considering the open/close of the key as the keying waveform. That open/close is shaped by the rig to give it a smooth rising and falling wave shape. That shaped waveform is the keying waveform and is the input to the system.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

The opening and closing of the key is not the keying waveform. It is the driving function. It is the system input. Everything done after that is a system response to that driving function. That driving functino is a square wave with a period and a duty cycle.

If that square wave is shaped by the rig then the rig is applying a system response against the driving function to come up with an output response.

With no key opening and closing how would the system have anything to respond to?

You are trying to change places between the chicken and the egg. In this case you have to have the egg to hatch before you can have a chicken to fry.



<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
When I read Chen’s analysis, I see the following. The keying waveform, which is the modulation to the RF stage, he describes as a square (or rectangular wave) that is convolved with a wave-shaping window function. The square/rectangular wave sets the overall pulse width while the convolution with the wave-shaping window function sculpts the rising and falling shape of the keying function. The convolution in the time domain is, as Chen points out, a simple multiplication in the frequency domain after the FT is taking of the square/rectangular wave and the wave-shaping window function.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Let's think about what is being said here. The comb function is a series of impulses in the frequency domain, lets say an impulse every 10 hz at an amplitude of 1. Now, what does a low pass filter look like in the frquency domain? It looks like a box from -wf to +wf and lets say the gain of the function (i.e. the height of the box) is also 1. Lets say the bandwidth of our box is 500hz, i.e. from -250hz to +250hz around the center frequency. Now do the multiplication in the frequency domain. Impulses further away from the center than -250hz, i.e. from -260hz, -270hz, etc will be multiplied against a filter response that is zero. So we get zero for a result. From -250hz to +250hz we get an impulse of 1 every 10hz multiplied by a filter function that is 1 so we get impulses of 1. For frequencies higher than 250hz we get multiplications that are zero.

So what do we wind up with? We go from a comb driving function with impulses from negative infinity to positive infinity (i.e. infinite bandwidth) to a bandwidth limited response that only has impulses between -250hz and 250hz.

Now, lets go from that easy example to one with a square wave with impulses at every odd harmonic from negative infinity to positive infinity but whose amplitudes gradually decrease as 1/n. Assume the same filter function with a gain of 1. What do we get when the two are multipled together in the frequency domain? You get exactly the same thing as before. Any impulses outside the -250hz to +250hz bandwidths have multiplication results of zero and impulses inside the -250hz to +250hz bandwidth have the same amplitude as before the multiplication. The result? A square wave missing higher frequency harmonics which results in a bandwidth limited output response. It is a square wave but now with rise times caused by the bandwidth limiting.

Now, let's look at a raised cosine filter. In the time domain it looks kind of like a damped sine wave. In the frequency domain it looks like anything from a rectangular window to a mis-shaped partial cosine depending on the rolloff factor. The rolloff factors basically determine the bandwidth of the filter in the frequency domain and the amplitude of the filter when applied to impulses inside the filter bandwidth. If the rolloff factor is 1 you get the closest to a cosine shape so what do you get when you apply this to a square wave? Close in frequencies are not changed much, cos 0 = 1 so the fundamental and the 3rd harmonic are probably not changed much. As you go further out, the cosine approaches zero so those impulses near the filter cutoff get attenuated significantly. What's the result? Again, you wind up with an bandwidth limited output response that is a square wave with missing higher harmonics as well as harmonics that are still there but significantly attenuated.

Bottom line? None of these multiplications in the frequency domain result in any impulses being created further from the fundamental than were already there. The only way to increase the power bandwidth, at least that I can see, is for this multiplication in the frequency domain to somehow create frequencies that didn't exist in the driving function. In other words you have to have a system response function that is a generator as well as a filter. Do you know of any transmitter amplifiers or keying shaping circuits that are frequency generators as well as frequency filters?


<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
In Chen’s own words:

“Notice that for any smooth function that you use as a window, it's Fourier transform will fall faster than the envelope of the sin(x)/s function -- i.e., for a reasonable wave-shaping, the Fourier transform of the Gaussian falls off faster than 1/f where f is frequency.

Ergo, it is the wave-shaping function that is what governs the bandwidth of the shaped pulse, it is not the pulse width.”

That seems pretty clear to me. It is the shape of the rising and falling edge of the keying waveform that dominates the bandwidth, not the pulse width.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>


The shape doesn't determine the bandwidth other than by limiting the frequencies that can be passed through the system response function. I hope my analysis above shows that. The frequencies that appear in the driving function, which is all that the wave shaping filter has to work with, *are* determined by the pulse width, at least insofar as the pulse width is an indicator of the fundamental frequency of the square wave. For a 50% duty cycle, periodic square wave, the fundamental frequency is easy to calculate and demonstrates the theory quite well.

Remember that the square wave is a sort of damped sine wave in the frequency domain - that is a sinx/x function. All that Chen is saying is that a good window will reduce the amplitudes of the impulses of the square wave that are far away from the fundamental frequency even faster than they already do decrease!



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Then Chen goes on to discuss what happens when you have a train of pulses rather than a single pulse. He describes the keying waveform as a comb function convolved with the prototype keying function he described above.

Once again, in Chen’s own words:

“Again, from the Fourier Duality statement, the spectrum of a series of dits is just a product of the Fourier transform of the prototype shaped pulse and a comb in the frequency domain. Again, the spectrum of the window predominates and knocks out all the higher frequency components of the comb.”
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Yes, that is exactly what I have been saying. We agree totally. The window, i.e. the system response function, limits the bandwidth of the system. It takes the bandwidth of the driving function, i.e. a comb with an infinite frequency bandwidth, and *REDUCES* it. It doesn't make the bandwidth wider!



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That also seems pretty clear to me. The shape of the rising and falling edges of the keying function dominates the bandwidth for a series of dits, not the width of the pulses.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Nope. The shape of the output response is only a function of the multiplication of the driving function and the system response function. Yes, the shape, which includes the rising and falling edges, is a result of the multiplication of the two frequency domain responses but it isn't the *cause*, per se, of the bandwidth. The bandwidth is determined by *both* the driving function and the system response function.

Let's take it that one more step further. Let's suppose we still have that ideal 500hz bandwidth low pass filter. But let's also suppose we have a driving function that is a 1hz square wave. That square wave is make up of impulses at 1hz, 3hz, 5hz, 7hz, 9hz, 11hz, ..... etc. Now, what will the amplitude of the harmonic impulses be at the 250hz bandwidth edges of the filter? 1/249 or .004 if we assume 1 as the normalized maximum amplitude. Pretty small eh? What do you suppose dominates the power bandwidth of this square wave? Is it the system response function? Probably not. If you assume that the first 30 harmonics are the main power components, it's not even close.

In this case how can you say the rising and falling edges of the system response function has any impact on the bandwidth of the system output at all?



<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<,
Now, what did Chen have to say about Mickey’s calculations?

Chen: “I think your calculations are perfectly sound -- however, the window function that you are using is not the right one to use and therefore not attenuating the keying sidebands.”

Chen: “The problem is that sin(x)/x falls very slowly (envelope decays as 1/x) and therefore does not fall off fast enough to attenuate the keying sidebands enough, so your effective bandwidth is very wide.

From the mathematical viewpoint, the problem comes from the fact that there is a slope discontinuity when the pulse starts and another slope discontinuity when the pulse ends (even though there is no discontinuity in the function itself).

So, even though f(t) is continuous, f'(t) is not and that is allowing the spectrum of the prototype pulse to assume a very wide spectral shape.

I am sure that if you apply this second window function (raised cosine), everything will come out as the practical guys have measured on their spectrum analyzers.”
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Well, duh! What do you suppose the first derivative of a square wave is? It is a series of impulses. A series that extends from negative infinity to positive infinity in the frequency domain. This is nothing earth shattering. It *is* what makes a pure square wave output from a transmitter very wide, wider than it needs to be.

As I beleive Mickey pointed out, what he was doing was using an easily calculated example to demonstrate the theory. It is easier to start easy and gradually work your way into the harder stuff.




>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
That too is pretty clear: Mickey’s calculations are *mathematically correct* - in other words, he did not make an error in calculation. However, Chen states very clearly that the problem is Mickey’s choice of his window function, which has a slope discontinuity, and it is this slope discontinuity that causes the prototype pulse to “assume a very wide spectral shape”. And finally, Chen is very clear that if Mickey were to use a more suitable window function, he is sure that the calculations will agree with the spectrum analyzer plots.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>.

No, that is not what Chen is saying. He is saying Mickey didn't pick a window function that will limit the bandwidth as much as it could be limited. If Mickey's calculations are right then they are right. What Chen is saying is that the bandwidth could be even SMALLER than what Mickey calculated, not *bigger*.

Again, you don't have a choice in the driving function, it is a square wave. It is an open and close switch operation. It is the system response to this driving function that determines the output response bandwidth.

Do you honestly believe that most people don't know that a square wave has a very wide spectral shape? And that they don't know that a real-world 6db rolloff low pass filter is not a very effective filter?

Nothing Chen speaks of will INCREASE the output response bandwidth, it will only reduce it from what Mickey has calculated. You seem to have a disconnect here. Remember, Chen said that Mickeys filter window is "not attenuating the keying sidebands". Yet Mickeys bandwidths are already narrower than what we are seeing the measurements show. Chen's advice will only further narrow the bandwidth and make the discrepancy between the calculations and the measurements even worse!



>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Personally, I think that Mickey did an excellent job in his analysis and in presenting the information here. I think that there was a fundamental flaw in the underlying assumptions that the analysis was based on, and Mr. Chen pointed out what that flaw was – the choice of window function. My conclusion from Mr. Chen’s comments: if Mickey had chosen a more suitable window function (i.e. a window function that more closely represents the leading and trailing wave-shaping of a typical CW transmitter) his calculations would agree with Tom’s measurements on the spectrum analyzer.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

I agree Mickey did an excellent job! This is as good of a thread as I have seen for a long time!

Chen didn't point out any flaws, and I can't find any either. the only "flaw" might be that a simple low pass filter is not an efficient bandwidth shaper but I think everyone already knew that.

You still have the disconnect that Chen said Mickey could make the bandwidth smaller by using a different window and you are turning that into saying that Chen said Mickey could make the bandwidth WIDER by using a different window. Your conclusion and Chen's statements can't both be right.



>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I am not attacking Mickey here. I have tremendous respect for Mickey, and I commend him on the work that he did in his analysis. I certainly would not have discovered the source of disagreement between his calculations and Tom’s measurements, and only through reading Mr. Chen’s comments do I finally understand where the difference comes from.

Mickey - have I unfairly summarized Chen's comments, or have I misunderstood them?
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

I hope you will look closely at my explanation of the multiplication of a filter window and a square wave. I think you will find that the source of the difference between Mickey's calculations and Tom's measurements are still up in the air.

73,

tim ab0wr
 
RE: Bandwidth versus Keying Speed  
by W8JI on June 2, 2007 Mail this to a friend!
by AB0WR on June 1, 2007 Look at the original message. It's a 2.4wpm, 1hz square wave power bandwidth.


If the power bandwidth of a square wave, that's a waveform with the maximum number of harmonics and zero rise time, is 42hz but the power bandwidth becomes *higher* when the wave is bandwidth limited, i.e. a rise time is appears on the wave, then the whole world is upside down. That means we could generate higher and higher bandwidths by using longer and longer rise times. >>

This explains why we have the difference of perception. I tried earlier to get everyone on the same page but was obviously unsuccessful.

Indeed if we look at the energy distribution of a very slow square wave, we find what you are saying.

As I have said before the problem is nothing in the system cares about what happens in the long term. It does not affect the receiver bandwidth, it does not affect the transmitter bandwidth so far as distributed power. We always have to consider how the system behaves.

The job of any mathematical analysis is to provide a shortcut or another way of explaining the system, not to change how the system works or how we perceive the system works. It works as it does. We hear and observe what we hear and observe.

When the application of a shortcut calls our observation of reality a liar, it's time to change the application or to just admit it doesn't apply to the real world we live in.

I built my first real transmitter and sent CW on the air in 1962 on 7175 kHz. Now in 2007 I'm transmitting a carrier again on 7175 kHz.

There are about 31.5 million seconds in a year. 1.42 billion seconds in 45 years. How can that very slow square wave with a period of 45 billion seconds produce a keyclick that causes problems 2 kHz away?

It seems to me on a lesser time scale we have the same problem. Of course the energy in the carrier, if we send slow enough, overwhelms or dwarfs the sidebands that cause problems.

That slowing does not change the communications system and the bandwidth that system occupies or requires. The bandwidth required is the bandwidth needed to pass the rise and fall without altering the shape of the rise and fall.

It doesn't matter to the CW receiver or the operator how many gallons of water the carrier can heat over a twenty minute period (or even a ten second period) compared to the long term accumulated energy in the sidebands. It only matters what the very short term level of the sidebands are compared to the peak envelope transmitter power, and that is relatively constant.

Neither the receiver nor the operator accumulate energy over an infinite time period, they don't even do it for milliseconds. It's a peak power problem.

73 Tom
 
Bandwidth versus Keying Speed  
by K5MC on June 2, 2007 Mail this to a friend!
I believe I have a graduate student lined up this summer to help me calculate the power/occupied bandwidths of the various keying waveforms that W7AY has mentioned. Since the 5-ms rise time for the "sinusoidal" keying waveform in my article is the time required to go from 0% to 100% amplitude, we will use the same definition of rise time (rather than the more standard 10% to 90%) for the other keying waveforms we plan to study. Although I have no doubt that the power bandwidths of these other keying waveforms are more narrow than my "sinusoidal" waveform, I simply cannot believe that we will find that their power bandwidths remain "essentially" constant when the speed increases from 2.4 wpm to 30 wpm. Of course, we will report exactly what our calculations show.

Turning to the spectrum plots and occupied bandwidth data presented by W8JI, I continue to believe that the problem here is primarily the lack of frequency resolution by Tom's spectrum analyzer. I have seen that with my own eyes using spectrum analyzers as well as in computer simulations that approximate the Fourier transforms of signals.

For example, yesterday a couple of graduate students and I clearly observed the discrete line spectrum produced by a CW/ASK "transmitter" under "square-wave" keying. We used a Wavetek Model 180 function generator to produce a "raised" square-wave keying waveform just as I used in my calculations. The keying waveform from the Wavetek modulated the amplitude of a "high frequency" sinusoidal carrier wave produced by an HP 33120A signal generator. In addition to seeing the magnitude spectrum on the HP 3561A Dynamic Signal Analyzer, we observed the CW/ASK signal on a Tektronix 2445 oscilloscope. The fundamental frequency of the keying waveform was initially set to 10 Hz, giving us 10 dits per second or 24 wpm. The discrete spectrum we observed on the HP 3561A was exactly what the theory/mathematics says. When we increased the sending speed to 20 Hz (48 wpm), the frequencies of the respective sidebands moved out further from the carrier exactly as told by the Fourier series.

The carrier frequency was only 50 kHz when we saw these very nice looking discrete line spectra on the analyzer! Even though the HP 3561A is now over 15 years old, I believe it is still an excellent low frequency analyzer. According to the 3561A operating manual, with a frequency span of 2 kHz the analyzer's display resolution is 5 Hz. With a span of 100 kHz (the upper frequency limit of the 3561A), its display resolution is 250 Hz.

With the start and stop frequencies set to 49 kHz and 51 kHz, respectively, our display resolution was 5 Hz. Therefore, we were able to see the individual keying sidebands distinctly, starting with the first pair of sidebands plus and minus 10 Hz from the 50-kHz carrier! The noise levels between the various sidebands was probably 40 dB down or more, so there's no question that the "power" bandwidths for this particular "CW" transmitter using this particular spectrum analyzer would give results very close to my calculations.

We then set the carrier frequency to 3.5 MHz and observed the spectrum on an HP 8920A analyzer. With the frequency span of the 8920A set to 10 kHz (the lowest span available on the 8920A), we had to increase our sending speed up to around 2400 wpm (1,000 Hz modulating frequency or 1,000 dits per second) before we began to even see some distinct frequency components! At speeds below around 2400 wpm the analyzer's resolution was simply too low to properly display the actual discrete line spectrum being generated by the signal. I have also observed the very same effect when analyzing signals using MATLAB, a popular software package that estimates Fourier transforms via FFTs. If you do not have enough data points in your sampled waveform, the resulting spectrum calculated by the FFT will look very similar to what the students and I saw on the 8920A yesterday, both of which are very similar, in my opinion, to the plots posted by W8JI.

If every transmitter (from old tube rigs on up) ever tested by Tom with his spectrum analyzer indicates that the occupied bandwidth remains essentially constant no matter what the speed is, then obviously either the math model I assumed in my article is an extremely poor approximation to physical CW transmitters or there's something wrong in the measurement process. As I discussed above, I believe the problem is primarily due to the lack of frequency resolution in Tom's analyzer. Perhaps Tom can show us spectra displays from a tone-modulated AM transmitter. If I'm right, then the spectra displayed by his analyzer when testing an AM transmitter tone modulated using a sine wave at 10 Hz (corresponding to the fundamental frequency when sending 10 dits per second or 24 wpm), 25 Hz (60 wpm), and 40 Hz (96 wpm) will all look essentially the same when his analyzer is adjusted as he had it for his CW spectra plots. I believe this test should answer the question I have about Tom's spectrum analyzer. (I will do a similar test myself using the 8920A on Monday.) Hopefully everyone here will at least agree that an ideal analyzer under these conditions would display a distinct line spectrum corresponding to the carrier at 3.5 MHz, the upper sideband at either 10, 25, or 40 Hz above 3.5 MHz, and the lower sideband at either 10, 25, or 40 Hz below 3.5 MHz.

73, K5MC
 
RE: Bandwidth versus Keying Speed  
by W8JI on June 2, 2007 Mail this to a friend!
by K5MC on June 2, 2007 I believe I have a graduate student lined up this summer to help me calculate the power/occupied bandwidths of the various keying waveforms that W7AY has mentioned.>>


It might be helpful to look at a radio first.

<< Since the 5-ms rise time for the "sinusoidal" keying waveform in my article is the time required to go from 0% to 100% amplitude, we will use the same definition of rise time (rather than the more standard 10% to 90%) for the other keying waveforms we plan to study. Although I have no doubt that the power bandwidths of these other keying waveforms are more narrow than my "sinusoidal" waveform, I simply cannot believe that we will find that their power bandwidths remain "essentially" constant when the speed increases from 2.4 wpm to 30 wpm. Of course, we will report exactly what our calculations show.>>

But we already know what your logic, thought process, and application of formulas describe Mickey. Repeating that process isn't necessary. The results will always be the same.

<<Turning to the spectrum plots and occupied bandwidth data presented by W8JI, I continue to believe that the problem here is primarily the lack of frequency resolution by Tom's spectrum analyzer. I have seen that with my own eyes using spectrum analyzers as well as in computer simulations that approximate the Fourier transforms of signals.>>

You can believe it all you want Mickey but the resolution bandwidth of the analyzer is 10 Hz. If I do a occupied power measurement of a steady carrier from the same rig the result is an occupied BW of 30 cycles. If I repeat it with a narrower and more selective Selective Level Meter the occupied BW of the carrier is 15Hz.

Both tell me it is about 400-500 Hz for a string of dots, and while a receiver hears the clicks for a wider bandwidth since it has a wider filter it also does not change with speed so long as the speed isn't at an extreme limit.

I have a question. My IC-751A's SSB transmitter has an occupied BW of about 2kHz with normal speech. If I talk slower does the transmitter become narrower?

73 Tom

 
RE: Bandwidth versus Keying Speed  
by KE3HO on June 2, 2007 Mail this to a friend!
Tim,

If you choose a window function that is very broad in the frequency domain, it will intercept multiple teeth of the comb. As you key faster, it will intercept more and more teeth of the comb. You and Chen and I are all in agreement on this.

So what does that prove? It proves that if you choose a leading and trailing edge wave-shaping function in your CW transmitter that has a very broad FT then you have done nothing more than design the worlds best key-click generator. Chen pointed out that, mathematically, this is what Mickey has done. If you design your leading and trailing edge wave-shaping function so that it is narrow enough in the frequency domain that it only intercepts one tooth of the comb for the fastest keying speed that you are designing for, then your spectrum is the same at all keying speed - you only ever intercept one tooth of the comb. I can't put it any planer than that.

Yes, Mickey's analysis is exactly correct. His calculations are without error. The problem is that his analytical model is a model of an outstanding keyclick generator. This is what Chen is saying.

If Mickey had chosen a better window function, one that is narrower in the frequency domain, then the prototype pulse would only ever intercept one tooth of the comb for reasonable keying speeds and the spectrum would be completely independent of keying speed. Mickey chose a window function that was easy to calculate the FT of. Being easy to calculate is not a virtue if it does no represent something that you might actually use in the real world.

So why does Tom's 751 have a 500Hz signal at all keying speeds? Because that it the width of the sidebands generated by the leading and trailing edge pulse shaping function of the 751. The sidebands are generated by the leading and trailing edge pulse shape of the CW keying function, and are independent of keying speed so long as the FT of the pulse shaping window function is narrower than the spacing of the comb for your highest keying speed.

73 - Jim
 
RE: Bandwidth versus Keying Speed  
by AB0WR on June 2, 2007 Mail this to a friend!
w8ji:"Indeed if we look at the energy distribution of a very slow square wave, we find what you are saying"

Let me get this straight. You are saying that a rise time on a square wave indicates a higher bandwidth signal instead of a lower bandwidth signal?

I just want to be extremely clear on this point.

tim ab0wr
 
Bandwidth versus Keying Speed  
by W7AY on June 2, 2007 Mail this to a friend!
HI all,

I apologize if this adds more flames to the fire. (eHam finally allows me to post; I had not been registered earlier).

IMHO, KE3HO hits the nail right on the head.

A Fourier window is nothing more and nothing less than a low-pass filter which has a finite duration in the time domain.

You simply need to choose a window whose spectrum falls faster than both the spectrum of the sin(x)/x of the square wave pulse and the spectrum of a comb from the repetitive pulses.

Here is an experiment: tune in to a nice 35 wpm CW signal. Now crank your filter down to 150 Hz. Still perfectly copyable, no?

Which means that if I were to apply a 150 Hz brick-wall filter to the transmit signal, the other end will also be able to copy my 35 wpm CW fine, too.

Further, this 150 Hz filter would cut off any higher spectral components, whether they come from the sin(x)/x of the original square wave pulse, or from a comb.

I.e., you do not need to transmit all that wideband stuff to pass aural Morse information. Waveshaping the pulse is just one way to limit said bandwidth.

If you have a Macintosh, you can easily do this experiment using cocoaModem, since it transmits using J2A emission mode (audio CW that is translated to RF with an SSB transmitter) and it has a risetime slider. Send the output to the computer's speakers and listen to the generated Morse.

Just set the transmit Morse speed at some suitably high speed and then go to the configuration panel to adjust the rise time slider.

Even better, if you have a second Macintosh, just run that audio output of the first computer into a second computer that watches the spectrum of the signal in a cocoaModem spectrum window (which measures down to -100 dBFS).

In cocoaModem I had use a Blackman window to shape the prototype pulse. The risetime slider adjusts the width of the window so that the function rises from 10% to 90% to the stated risetime. For the default, I had used a 5 msec risetime, which seems to work well.

In Fourier transforms, first order discontinuities cases wide spectra, but second order discontinuities (slope discontinuities) also causes wide spectra.

That is why "good" window functions that DSP folks use are attempts to be maximally smooth and yet have finite duration.

For an example where slope discontinuity is harmful, take a look at John Grebenkemper's modification of the K2 here

http://home.pacbell.net/johngreb/improving_elecraft_keyingmod.pdf

Scroll down to the first figure and you can see that the original keying pulse (in red) has a bad slope discontinuity at the onset of the rising edge. John's modification creates a more gradual change. Several plots later, he shows the spectra for the different keying waveshapes.

I apologize again for wasting bandwidth and also for my poor English; it is not even my second language, HI.

Vy 73
Chen
 
Bandwidth versus Keying Speed  
by AB0WR on June 2, 2007 Mail this to a friend!
ke3ho:"If you choose a window function that is very broad in the frequency domain, it will intercept multiple teeth of the comb. As you key faster, it will intercept more and more teeth of the comb. You and Chen and I are all in agreement on this.

ke3ho:"So what does that prove? It proves that if you choose a leading and trailing edge wave-shaping function in your CW transmitter that has a very broad FT then you have done nothing more than design the worlds best key-click generator. Chen pointed out that, mathematically, this is what Mickey has done. If you design your leading and trailing edge wave-shaping function so that it is narrow enough in the frequency domain that it only intercepts one tooth of the comb for the fastest keying speed that you are designing for, then your spectrum is the same at all keying speed - you only ever intercept one tooth of the comb. I can't put it any planer than that. "

If all you allow through the system is one frequency how does that somehow turn into a wider bandwidth?

I agree that if you make your filter narrow enough all you will allow through is one frequency. There isn't any doubt about that.

I suspect the problem here is that you are confusing the time domain and the frequency domain. A raised cosine filter in the time domain looks like a damped sine wave. Really, it does. Look it up using Google if you don't believe me. You will find no rise time on the time domain response graph of the function at all.

Yet in the frequency domain the filter can be very narrow. It is the frequency domain response that best shows the bandwidth of a signal. And, yes, the spectrum you see will be the same for all keying speeds. But it won't be wider than the input signal bandwidth for any keying speed. It will be one frequency. (actually in the real world this is impossible because a single frequency which is never turned off or on can carry no intelligence at all).

You seem to be still stuck at trying to confirm that the rise time of an output response, as seen in the time domain, somehow generates harmonics that makes the signal bandwidth wider. It doesn't. The output response will always have a narrower bandwidth than the input driving function in this situation.


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Yes, Mickey's analysis is exactly correct. His calculations are without error. The problem is that his analytical model is a model of an outstanding keyclick generator. This is what Chen is saying.

If Mickey had chosen a better window function, one that is narrower in the frequency domain, then the prototype pulse would only ever intercept one tooth of the comb for reasonable keying speeds and the spectrum would be completely independent of keying speed. Mickey chose a window function that was easy to calculate the FT of. Being easy to calculate is not a virtue if it does no represent something that you might actually use in the real world.
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As I said, the filter can't be so narrow as to allow only one impulse through. This would be the same as having a non-varying carrier which, by definition, has zero bandwidth and no intelligence carrying capacity. That is what would make such a narrow filter something you wouldn't use in the real world.


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So why does Tom's 751 have a 500Hz signal at all keying speeds? Because that it the width of the sidebands generated by the leading and trailing edge pulse shaping function of the 751. The sidebands are generated by the leading and trailing edge pulse shape of the CW keying function, and are independent of keying speed so long as the FT of the pulse shaping window function is narrower than the spacing of the comb for your highest keying
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

I disagree. As I pointed out in my message explaining output responses from filter functions and square wave driving function, you wind up with a limited bandwidth keying function, i.e. there are only so many odd harmonics that get through. The limited frequency bandwidth of the signal (along with the amplitude relationship between the harmonics) is what determines the shape of the waveform in the time domain. The "shape" doesn't generate anything, it only "describes" what is happening.

It might be instructive to actually graphically convolve a raised cosine response function (a damped sine wave) with a square wave driving function in the time domain. I think it will better demonstrate that it is the convolving of the two functions that determines the shape of the resulting output function and that it isn't the shape of the output function that determines itself, that would violate causual rules.

That keying function, with a limited number of odd harmonics, becomes a driving input function for the next stage in the system.

Modulation in a linear system is done by varying the gain of the system using one input function in order to modulate the other input function. If r(t) is the output and f1(t) is one input and f2(t) is the other input you set the gain of the system to be G(t) = K x f1(t). Then r(t) is:

r(t) = G(t) x f2(t) = Kf1(t)f2(t)

Multiplication in the time domain is convolution in the frequency domain. If w0 is the carrier frequency, i.e. f2(t) then you wind up with a w0+w and a w0-w term for every frequency that exists in the keying waveform, f1(t). (you also have a -w0+w and a -w0-w set of terms but negative frequencies don't concern us in a real transmitter). So what do you get? If your output response from the keying circuity wound up with the fundamental, the 3rd harmonic, and the 5th harmonic you would have sidebands consisting of [w0 + fundamental, w0 + 3rd harmonic, and w0 + 5th harmonic] and [w0 - fundamental, w0 - 3rd harmonic, and w0 - 5th harmonic].

The actual bandwidth becomes twice the bandwidth of the keying waveform because of the upper and lower sidebands that are generated. If you read Mickey's original message I think you will find that he accounted for this in his calculations.

The modulation function still doesn't generate any additional frequencies that aren't already in the driving signal. If your original driving function was a 2hz square wave and you allowed only two odd harmonics through the sidebands would contain frequencies of 2hz, 6hz, and 10hz. The total absolute bandwidth of the output signal would be 20hz.

The "shape" of the keying signal in the time domain did nothing except describe the number of odd harmonics existing in the signal. It didn't generate *anything* in the modulation process beyond what was already there.

I think we agree that an output response square wave with a 5ms rise time indicates a 600hz system bandwidth (approximately). Where I think we disagree is that you say that the rise time generates the bandwidth and just stop there. I say the rise time is the result of an input driving function and a bandwidth-limited system response function, the rise time is not a *cause* but a result. I don't accept that output responses "create" anything, output responses are *created*. That means that the driving function or the system response function is something other than what Mickey and I are looking at.

tim ab0wr
 
RE: Bandwidth versus Keying Speed  
by W8JI on June 2, 2007 Mail this to a friend!
Thank you Chen.

I looked at your page and the diagram of the sidebands within the curve set by the rise and fall shape agree with what my spectrum measurements show if I synchronize my analyzer time base to the dot generator.

I see nothing on your page that disagrees with real world equipment I have measured, and it all fits the practical world.

This has consumed too much time and I think it won't go in a useful direction for anyone, so I've said about all I can say for now.

As you correctly point out the rise and fall is very critical and even a very small glitch can cause a large problem with CW bandwidth. Some radios are too fast, some have poor shapes from ALC, some have poor shapes from poor filtering of the harmonics in the modulating waveform.

As long as we don't pretend sending slower fixes a radio and makes it narrower, I am happy. I agree a 5ms rise and 5ms fall is fast enough. Some radios that allow users to set the rise and fall add both times together, so a 5ms rise and 5ms fall is obtained at a 10ms setting.

73 and thanks
Tom

73 Tom





 
Bandwidth versus Keying Speed  
by K5MC on June 2, 2007 Mail this to a friend!
W8JI: If I do a occupied power measurement of a steady carrier from the same rig the result is an occupied BW of 30 cycles. If I repeat it with a narrower and more selective Selective Level Meter the occupied BW of the carrier is 15Hz.

Tom, I assume you are giving us two different values of occupied/power bandwidth here. (For example, the 99.75% power bandwidth is 30 Hz and the 99.0% power bandwidth is 15 Hz?) I would appreciate knowing the percentages if you have that information handy.

I have little doubt that a 10-Hz sine wave modulating a typical ham AM rig would be doomed to failure in terms of actually seeing the two sidebands distinctly from the carrier on a spectrum analyzer. The spectral purity of the high frequency carrier is simply not good enough. I wonder how high the tone frequency would have to be before we would see on a spectrum analyzer the classic carrier/two sidebands spectral lines that many of us see in our minds when we think of tone modulated AM? 50 Hz? 100 Hz? (I remember from teaching our senior level communications lab several years ago that the tone frequency has to be "pretty" high before students really begin to see the sidebands distinctly from the carrier on the HP 8920A, but I don't believe this particular instrument is the last word on RF spectrum analyzers!)

W8JI: I have a question. My IC-751A's SSB transmitter has an occupied BW of about 2kHz with normal speech. If I talk slower does the transmitter become narrower?

If you do it under what I consider "controlled laboratory conditions" then I would say YES! If you record your audio signal that modulates the SSB transmitter when you send your fixed-length message in real time, then when you send that same message again at the slower rate by dropping the tape recorder speed to 50%, the spectra components will be only 50% along the frequency axis compared to the original message. For a very simple example, let's assume I can whistle a pure tone at 2 kHz. If my original signal is a 2-kHz whistle for 1 second, then when I repeat that signal at half the recorded speed, it will be a 1-kHz whistle that lasts 2 seconds. In sending this "message" (I concede the point that the "information" of this message is very low!) the second time I used half the bandwidth for twice as long.

Now let me ask you a question. Does the bandwidth of an FM signal depend only on the amount of frequency deviation or shift? For example, if I limit the instantaneous frequency of my FM signal to be plus or minus 75 kHz of the center frequency, is my bandwidth confined to be within 150 kHz no matter whether I use a 1-kHz tone or a 10-kHz tone as the modulating signal?

AB0WR: Nothing Chen speaks of will INCREASE the output response bandwidth, it will only reduce it from what Mickey has calculated. You seem to have a disconnect here. Remember, Chen said that Mickeys filter window is "not attenuating the keying sidebands". Yet Mickeys bandwidths are already narrower than what we are seeing the measurements show. Chen's advice will only further narrow the bandwidth and make the discrepancy between the calculations and the measurements even worse!

KE3HO: Mickey - have I unfairly summarized Chen's comments, or have I misunderstood them?

Tim and Jim, I appreciate your comments very much. It's getting really hard for me to keep up with everyone's detailed comments! Jim, as W7AY said himself, I believe you have a good understanding of Chen's comments and I also agree with almost everything Chen has said. The main thing I'm still wondering about is the spectrum plots posted by Tom. As Tim alludes to in his comments above, the 99.1% power bandwidths I calculated for "square-wave" keying at 2.4 wpm and 30 wpm were 42 Hz and 525 Hz, respectively. Tom's measurements are showing that the 99% power bandwidth is about 490 Hz at 24 wpm (10 dits per second) and is adamant that the 99% power bandwidth does not vary with the speed. However, if my model is approximately valid, then as Tim points out, 42 Hz is much smaller than 490 Hz! What's going on here?

As I've already said, I think Tom's spectrum plots are not consistent, although I do concede that his analyzer print outs clearly indicate a "resolution bandwidth" of 10 Hz. If this resolution is referring to the display resolution at 3.5 MHz over a 3 kHz span, then that is very good indeed! If Tom's plots are accurate, then the math model I used is obviously not valid for real world CW rigs, even for the special case of "square-wave keying. (And I'm sure that some actual rigs over the years have been close to that extreme case!)

That's why I was wondering what Tom's analyzer shows for a "good" AM transmitter when tone modulated at low frequencies. Obviously the spectral purity of the high frequency carrier is a limiting factor, but I'm not convinced that Tom's analyzer is not showing the effects of spectral "leakage" due to the finite data record along with the various other pitfalls when making measurements with even the best available spectrum analyzers.

In theory, at least, we should be able to look at the keying envelope of the output CW signal from an actual transmitter on an oscilloscope and model the signal mathematically as a function of time by finding its Fourier series coefficients just as I did with my assumed keying waveforms. I have access to some digital scopes at my school that should be able to do this.

I will save some comments I have regarding fundamental issues of bandwidth versus rate of information (speed) for a later post.

73, K5MC
 
RE: Bandwidth versus Keying Speed  
by KE3HO on June 2, 2007 Mail this to a friend!
Mickey,
<< The main thing I'm still wondering about is the spectrum plots posted by Tom. As Tim alludes to in his comments above, the 99.1% power bandwidths I calculated for "square-wave" keying at 2.4 wpm and 30 wpm were 42 Hz and 525 Hz, respectively. Tom's measurements are showing that the 99% power bandwidth is about 490 Hz at 24 wpm (10 dits per second) and is adamant that the 99% power bandwidth does not vary with the speed. However, if my model is approximately valid, then as Tim points out, 42 Hz is much smaller than 490 Hz! What's going on here? >>

Here is my take on this, in light of what Chen has taught me on this subject in the last couple of days. Changing the keying speed spreads out the teeth of the comb function in the frequency domain. The spectral bandwidth of the output signal is still dominated by the window function. You can spread the comb function out as much as you want, but you will still have your window function overlapping just one tooth of the comb. The bandwidth of the resulting CW signal is dominated by the window function, the shape of the rising and falling edge of the keying waveform, at any speed until you get up to very high speeds where your window function intercepts two or more teeth of the comb. Make your sending speed as slow as you want, the bandwidth of the signal will STILL be set by the rising and falling edges of the keying waveform.

If you look at it another way, as we did early in this thread, during the rise time of the keying function the carrier is modulated by the rising waveform and the sidebands are determined SOLELY by the shape of that rising edge of the keying waveform. Same holds for the falling edge. During the tc period where the keying waveform is constant, the carrier is unmodulated and the bandwidth is determined by several factors such as the frequency stability of the oscillator, phase noise, amplitude stability of the PA, and maybe some other factors too.

The theory and the practical part agree completely.

73 - Jim
 
RE: Bandwidth versus Keying Speed  
by W8XR on June 3, 2007 Mail this to a friend!
Tim,

Well put.

I've had a couple of comments off-list from folks that are a little intimidated by some of the DSP terms in this discussion and I've shared a more intuitive approach in an article that I've been working on that echos your comments.

So for those of you that are looking for a little less technical version of this discussion, (with a tad less shouting), please see: <http://members.toast.net/mark.amos/CW%20Bandwidth%20Analysis.pdf>

Thanks again for all the constructive comments in the thread and off-forum.

Mark
W8XR
 
RE: Bandwidth versus Keying Speed  
by W8XR on June 3, 2007 Mail this to a friend!
Oops again - not enough coffee yet:

JIM,

Well put.

I've had a couple of comments off-list from folks that are a little intimidated by some of the DSP terms in this discussion and I've shared a more intuitive approach in an article that I've been working on that echos your comments.

So for those of you that are looking for a little less technical version of this discussion, (with a tad less shouting), please see: <http://members.toast.net/mark.amos/CW%20Bandwidth%20Analysis.pdf>

Thanks again for all the constructive comments in the thread and off-forum.

Mark
W8XR

 
RE: Bandwidth versus Keying Speed  
by KE3HO on June 3, 2007 Mail this to a friend!
Mickey,

Shortly after posting my last comment, I reread your previous comment and I realized that you were talking about the square wave keying, not the window-shaped keying. I am doing some FT calculations to see what numbers I come up with.

Jim
 
RE: Bandwidth versus Keying Speed  
by KE3HO on June 3, 2007 Mail this to a friend!
Mickey,

I have calculated the FT of a pulse 0.490 sec wide and a pulse 0.030 sec wide and the graphs lay right on top of each other. The envelope is the same, all that is different is the spacing of the lobes. I don't see anything to indicate that one has a bandwidth of 42Hz and the other 525Hz.

73 - Jim
 
Bandwidth versus Keying Speed  
by K5MC on June 3, 2007 Mail this to a friend!
KE3HO: I have calculated the FT of a pulse 0.490 sec wide and a pulse 0.030 sec wide and the graphs lay right on top of each other. The envelope is the same, all that is different is the spacing of the lobes. I don't see anything to indicate that one has a bandwidth of 42Hz and the other 525Hz.

Jim, if FT means Fourier transform, then you have totally lost me. I'm looking on page 81 of Lathi's book right now and he clearly shows that the "essential" bandwidth (such as the 99% energy bandwidth) of a single gate (rectangle) pulse is inversely proportional to the pulse's duration. The Fourier magnitude spectrum plot of a 0.490-second pulse is "stretched out" much further than that of a 0.030-second pulse. (I'm talking about the actual baseband pulses here, which I referred to as the "square-wave" keying waveforms in my article.) If what you are saying is true, then every signal analysis textbook I have will have to be rewritten.

73, K5MC
 
Bandwidth versus Keying Speed  
by K5MC on June 3, 2007 Mail this to a friend!
Here is a very interesting email I just received from SM0AOM.

73, K5MC

SM0AOM: I have been following the discussion on the "keying speed vs bandwidth" subject on eham.net with great interest. As you may have found, I support your and others view that the keying or modulation rate indeed have an influence on the bandwidth of the A1A emission.

It may well be that the generation of "key clicks" is primarily a function of the lack
of proper rise and fall times in the keying envelope function, but I find from a
practical radio engineering and regulatory point of view that the discussion somewhat has gotten out of hand.

The A1A emission bandwidth as used in the ITU Radio Regulations assumes some fundamental properties of the keying shaping function in order to be valid, the most important that the slopes are free of discontinuities.

The examples used by i.a. W8JI are not very well connected to the assumptions used in the ITU-RR, as the keying slopes are not discontinuity-free, and also that the "build-up" or rise time is much faster that needed for a given keying speed or modulation rate. In the ideal world, these times should be a fraction (10 - 20 %) of the time of the shortest signal element used.

For you consideration, I am attaching the latest version of the CCIR/ITU-R Recommendation SM.328 that I was able to find, and also a scan from the Telefunken literature that I referred to earlier. It shows keying spectra of a 40 Baud (about 50 WPM) A1A emission without (left) and with (right) application of the CCIR keying shaping. The "resolution bandwidth" was well below 10 Hz in these spectra. Note that the "sidelobes" that show up in W8JI:s spectrum plots are absent.

It seems that the detalied regulations imposed by the FCC can lead to interesting consequences. If it should be proven that all A1A or CW emissions,regardless of keying rate, have 500 Hz occupied bandwidth the legal framework for band segmentation may very well "fall apart". In Europe, on the other hand, we are mostly not affected by such details any longer.

As a side-effect of telecoms market deregulation in Sweden, all references to the ITU-RR were removed from the domestic amateur radio regulations, with the consequences that suddenly there were no technical requirements any longer on amateur radio emissions. As long an emission with sidebands is contained within the band limits, it can have any spectral contents, which means that "key-clicks" or excessive bandwidth are not illegal in any sense.

Due to "lack of interest" from the regulators, any regular monitoring of the amateur radio bands also has come to an end, as amateur radio in Sweden has become "license-exempt" and therefore has no right to file interference complaints.

Finally, as the interest in A1A emission bandwidth question may not be entirely confined to the American continent only, it may be appropriate to initate a "re-write" of both the relevant parts of the ITU-R Recommendation SM.328 and the the Radio Regulations based on the argumentation put forward. The proper way to do this would be to get the FCC/US Government to file a petition to the ITU Secretariat to initiate an Interim Working Party (IWP) to analyze the question within the framework of the Study Group I.

There may however be practical problems to convene such an IWP, as the interest for the emission characteristics of A1A can be expected to be very small outside the amateur radio community.

It is most unfortunate that Peter, G3RZP, still is in hospital and cannot comment on this matter on eham.net. He has a much longer and more recent affliation with the ITU-R Study Groups than I have.

Sincerely,

Karl-Arne Markstrom
SM0AOM
 
RE: Bandwidth versus Keying Speed  
by W8JI on June 3, 2007 Mail this to a friend!
A few people can post whatever they want based on any analysis they put forth, but that does not change how the systems we all use work.

In the CW systems we all use and have all used, the bandwidth of the signal at a minimum is ALWAYS determined by the shape and duration of the rise and fall. The keyclick at the start and fall has **exactly** the same distributed energy or peak enevlope power at a give bandwidth away from the carrier regardless of keying speed.

This is because that transition point and the sidebands generated to accommodate that transition in level does not change.

Even if a person's logic or mind cannot wrap around that very simple concept, absolutely ANYONE on the face of this earth with a receiver having narrow filters and a transmitter can indeed confirm what I say is true.

It is the nature of CW receivers that they cannot store the energy from a click until the next click come along, except in the AGC system. The AGC being a peak hold system regustes and holds the peak level, but does not add successive clicks to the voltage unless it has slow attack time. But once it is up, it is up and it doesn't matter if one more click per second follows or 40 clicks per second follow. The IF and audio processing right through the CW operator’s brain cannot store the energy of the carrier or the click. A faster or slower repletion of clicks simply means they occur more often or less often, but the level and bandwidth is exactly the same. Only when the speed is so fast or slow the envelope rise and fall changes, or if the clicks are so infrequent most of the desired signal can be copied without harm, are clicks impacted by speed.

So what we are left with is a click of constant amplitude regardless of speed; with the offset or bandwidth of that click tied 100% directly to the envelope transition formation. The sole exception would be another defect like FM’ing, Hum, or composite noise; but there are very few radios where flaws in the nature of the carrier dominate the strong signal produced by the rising and falling edges. Those radios are the rare exception and are caused either by serious design errors (like the IC-775DSP where the VCO seeps during the transition) or defects unique to a particular radio. In such a case the bandwidth of the envelope rise and fall sets a lower bandwidth limit, while the spurious or purity issue extends the bandwidth even further.

Anyone can measure the effects I described above.

Without spending the time to do this all the good things that have been accomplished over the past few years will be turned aside and a few people really trying to understand how this all works will walk away either confused or with a distorted view of what actually happens.

For all those who think the bandwidth changes with speed, I suggest they do a few simple experiments. That will solve the whole issue.

It’s just totally beyond me why anyone would spend so much energy arguing a point endlessly without making some attempt to confirm it through experiment.

It sounds to me like people want reality to change and conform to what they explain, instead of observing the real world effect and explaining it. That’s not good science. It certainly does not advance the state of the art or help anyone. It is harmful, not helpful.

73 Tom



 
RE: Bandwidth versus Keying Speed  
by W9AC on June 3, 2007 Mail this to a friend!
W8JI:

> "It’s just totally beyond me why anyone would spend so much energy arguing a point endlessly without making some attempt to confirm it through experiment..."

To Tom's point, the Scientific Method demands the testing of a theorem or hypothesis. Theories which cannot be tested, because, for instance, they have no observable ramifications, do not qualify as scientific theories. Those who have been part of this discussion and who are engaged in the study and/or teaching of advanced academia have had exposure to the Scientific Method since the time of their first studies in elementary school.

The Scientific Method requires that a hypothesis be ruled out or modified if its predictions are clearly and repeatedly incompatible with experimental tests.




 
Bandwidth versus Keying Speed  
by K5MC on June 3, 2007 Mail this to a friend!
W8JI: In the CW systems we all use and have all used, the bandwidth of the signal at a minimum is ALWAYS determined by the shape and duration of the rise and fall. The keyclick at the start and fall has **exactly** the same distributed energy or peak enevlope power at a give bandwidth away from the carrier regardless of keying speed.

Tom, let's agree to call the bandwidth you describe above as the "keyclick" bandwidth so that we can all talk the same language. I have no problem or disagreement with what you are saying regarding the "keyclick" bandwidth. I've tried to make that point clear from day one. At the end of my article I said that the concept of "power/occupied" bandwidth as defined in Couch's textbook does not say that the strength of the individual key clicks heard decrease as the sending speed is lowered.

I'm certainly willing to learn from you and anyone else that posts comments here. Among a number of hams, SM0AOM has been very helpful to me. Here's a quote from an email that Karl-Arne sent me a few hours ago:

SM0AOM: For you consideration, I am attaching the latest version of the CCIR/ITU-R Recommendation SM.328 that I was able to find, and also a scan from the Telefunken literature that I referred to earlier. It shows keying spectra of a 40 Baud (about 50 WPM) A1A emission without (left) and with (right) application of the CCIR keying shaping. The "resolution bandwidth" was well below 10 Hz in these spectra. Note that the "sidelobes" that show up in W8JI:s spectrum plots are absent.

Unfortunately, eham doesn't allow me to post pictures, but I will be happy to forward the spectrum plots from Karl-Arne/Telefunken to anyone via email. (My email address is k5mc@arrl.org) Just as SM0AOM says, the two oscillograms from an actual transmitter clearly show the distinct keying sidebands (the discrete line spectrum) rather than continuous spectra plots as posted by W8JI.

It's finally becoming clear to me that there are some significant differences in the keying characteristics between various CW rigs. However, there's no doubt in my mind that the assumptions I used in my article will provide the correct value of the "power" bandwidth for equipment having the keying characteristics shown in Karl-Arne's oscillograms. For all of the CW rigs that have continuous spectra rather than discrete line spectra, the Fourier series approach that I used in my article will obviously not work.

I really hope that everyone will try to remember that Tom's "keyclick" bandwidth is not the same thing as the "power" bandwidth as defined by Couch [1]. I will try to stop using the term "occupied" bandwidth as being equivalent to Couch's "power" bandwidth.

[1] Leon W. Couch, Digital and Analog Communication Systems, 7th ed., Pearson Prentice Hall, 2007.

73, K5MC
 
Bandwidth versus Keying Speed  
by K5MC on June 3, 2007 Mail this to a friend!
W8JI: I have a question. My IC-751A's SSB transmitter has an occupied BW of about 2kHz with normal speech. If I talk slower does the transmitter become narrower?

K5MC: If you do it under what I consider "controlled laboratory conditions" then I would say YES! If you record your audio signal that modulates the SSB transmitter when you send your fixed-length message in real time, then when you send that same message again at the slower rate by dropping the tape recorder speed to 50%, the spectra components will be only 50% along the frequency axis compared to the original message. For a very simple example, let's assume I can whistle a pure tone at 2 kHz. If my original signal is a 2-kHz whistle for 1 second, then when I repeat that signal at half the recorded speed, it will be a 1-kHz whistle that lasts 2 seconds. In sending this "message" (I concede the point that the "information" of this message is very low!) the second time I used half the bandwidth for twice as long.

K5MC: Now let me ask you a question. Does the bandwidth of an FM signal depend only on the amount of frequency deviation or shift? For example, if I limit the instantaneous frequency of my FM signal to be plus or minus 75 kHz of the center frequency, is my bandwidth confined to be within 150 kHz no matter whether I use a 1-kHz tone or a 10-kHz tone as the modulating signal?

I'm still looking forward to hearing from W8JI regarding the comments above.

73, K5MC
 
Bandwidth versus Keying Speed  
by AB7E on June 3, 2007 Mail this to a friend!

W8JI:

"It’s just totally beyond me why anyone would spend so much energy arguing a point endlessly without making some attempt to confirm it through experiment."


I'm an electrical engineer myself and totally believe in the absoluteness of mathematics, at least in the context of this discussion, but those who put their faith exclusively in the results of <their> mathematical analysis without even considering whether they have misapplied it seem even less likely to be influenced by real world measurements. If none of the several intuitive explanations put forth here in this thread so far have convinced them they have missed something, why should a measurement that they can so easily attribute to other factors do so?

I'm astounded that supposedly rational people can claim that speeding up the rate of keying transitions, without changing the nature of the individual transitions themselves, can affect the bandwidth that is affected. It's funny how Fourier analysis, which was developed to give us a quantified understanding of observable physical behavior, can be so erroneously applied as to completely contradict that same observable behavior.
 
Bandwidth versus Keying Speed  
by K5MC on June 3, 2007 Mail this to a friend!
KE3HO: I have calculated the FT of a pulse 0.490 sec wide and a pulse 0.030 sec wide and the graphs lay right on top of each other. The envelope is the same, all that is different is the spacing of the lobes. I don't see anything to indicate that one has a bandwidth of 42Hz and the other 525Hz.

K5MC: Jim, if FT means Fourier transform, then you have totally lost me. I'm looking on page 81 of Lathi's book right now and he clearly shows that the "essential" bandwidth (such as the 99% energy bandwidth) of a single gate (rectangle) pulse is inversely proportional to the pulse's duration. The Fourier magnitude spectrum plot of a 0.490-second pulse is "stretched out" much further than that of a 0.030-second pulse. (I'm talking about the actual baseband pulses here, which I referred to as the "square-wave" keying waveforms in my article.) If what you are saying is true, then every signal analysis textbook I have will have to be rewritten.

I meant to say that the magnitude spectrum plot of the 0.030-second pulse is "stretched out" much further than that of a 0.490-second pulse. That is, the "essential" or "energy" bandwidth (as defined in electrical engineering textbooks!) of the 0.030-second pulse is significantly larger than that of the 0.490-second pulse.

Much of the debate concerning my article has obviously been created because of the different terminology used by the various posters. I have about worn down my keyboard typing "power bandwidth" rather than merely "bandwidth" because I wanted everyone to understand that there are many different definitions of bandwidth in the signal analysis/communications world. AB0WR, W1YW, and SM0AOM, in particular, have really understood the purpose of my article because they are electrical engineers by formal training and experience.

73, K5MC
 
RE: Bandwidth versus Keying Speed  
by AB0WR on June 3, 2007 Mail this to a friend!
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<,
ab7e:"I am an electrical engineer myself and totally believe in the absoluteness of mathematics, at least in the context of this discussion, but those who put their faith exclusively in the results of <their> mathematical analysis without even considering whether they have misapplied it seem even less likely to be influenced by real world measurements. If none of the several intuitive explanations put forth here in this thread so far have convinced them they have missed something, why should a measurement that they can so easily attribute to other factors do so?

I'm astounded that supposedly rational people can claim that speeding up the rate of keying transitions, without changing the nature of the individual transitions themselves, can affect the bandwidth that is affected. It's funny how Fourier analysis, which was developed to give us a quantified understanding of observable physical behavior, can be so erroneously applied as to completely contradict that same observable behavior. "
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Rather than just denigrate those who ARE trying to understand what inputs and transfer functions are causing the output function why don't you tell us what YOUR model of the input driving functions and the system transfer functions are?

You say you totally believe in the absoluteness of mathematics and then turn around and speak of having faith in "intuitive explanations"?

If you are an electrical engineer you should have some training in the analysis of linear systems. You should remember than in the frquency domain Output(s) = Input(s)Transfer(s).

So far all I have heard is the "intuition" that the output function causes the output function because it just does. I have seen no mathematical modeling from anyone making that "intuitive" claim, however. The only math that I have seen, and it has been confirmed by everyone so far, is that a square wave of fundamental frquency w0 has frequency components made up of w0 and all odd harmonics. And those odd harmonics have amplitudes determined by a 1/n factor.

I have yet to see anyone show any math as to how that all square wave input driving functions, of any fundamental frequency, gets transformed by a transfer function into a bandlimited waveform of about 500hz.

Instead of depending on the "intuitive" explanation that the output causes the output, tell us what your Input(s) and Transfer(s) model is that generates the output function we see on the spectrum analyzer.

Then perhaps we'll see the discussion get furthered rather than just see continued denigrations of how those actually using the math are "irrational".

ab7e"I'm astounded that supposedly rational people can claim that speeding up the rate of keying transitions, without changing the nature of the individual transitions themselves, can affect the bandwidth that is affected."

You are astounded that square waves of varying fundamental frequences (i.e. "speeding up the rate of keying") have different power bandwidths? When and where did you get your electrical engineering degree?

tim ab0wr
 
RE: Bandwidth versus Keying Speed  
by WA0LYK on June 3, 2007 Mail this to a friend!
>>W9AC
>>>>W8JI:
>>>>
>>>>> "It’s just totally beyond me why anyone would
>>>>spend so much energy arguing a point endlessly
>>>>without making some attempt to confirm it through
>>>>experiment..."

>>To Tom's point, the Scientific Method demands the
>>testing of a theorem or hypothesis. Theories which
>>cannot be tested, because, for instance, they have no
>>observable ramifications, do not qualify as
>>scientific theories. Those who have been part of this
>> discussion and who are engaged in the study and/or
>>teaching of advanced academia have had exposure to
>>the Scientific Method since the time of their first
>>studies in elementary school.

>>The Scientific Method requires that a hypothesis be
>>ruled out or modified if its predictions are clearly
>>and repeatedly incompatible with experimental tests.

What you are saying is that every text book written in the last 100 years needs to be tossed out and replaced by the hypothesis that the input rise time of a square wave defines the bandwidth and frequencies included, not the fourier transform of a periodic wave.

I'm sorry, but there will need to be a lot more peer review before this is done. I have not seen one engineer or scientist publish even an article here or post on this thread recommending that W9CF's mathemetics be used to define the bandwidth of a modulated signal in all new textbooks. I wonder why?

I had a long discussion with AB0WR about this. There appear to me to be several things at work here.

One, look on the ARRL web page for reviews of transmitters. You will find that the keying waveform IS NOT duplicated exactly on the output envelope. By definition, this means the transmitter as a system is non-linear. What is the predominate effect of a non-linear sytem? It is intermod products. These have nothing to do with the rise time, only the frequency products contained in an input waveform.

K5MC has already defined the frequency products for low speed keying using fourier analysis and they don't extend out near far enough to generate the kinds of bandwidth W8JI observes, but intermod products would. The only alternative is if you are ready to say that the fourier analysis of a periodic waveform or even a step function is invalid.

Two, if rise times are what causes the minimum bandwidths of 200 - 400 Hz, then how do signals like psk31, psk63 or psk125 achieve such small bandwidths? You can't just say that the math model for determining CW bandwidth by analyzing the rise times applies to CW only. It must apply to any modulating waveform like psk, rtty, etc.

W8JI mentions the FT1000's well known problem with key clicks on his web page and attributes it to rise time problems. This isn't the case. Have a look at Inrad's web page and they explain the problem. The FT1000's ALC doesn't act fast enough and a severe power spike occurs at the leading edge of a CW waveform. The spike is large enough to drive the amps into saturation causing intermod products to be generated.

The Inrad site also mentions the OmniVI+ as having an ALC problem causing distortion of the CW waveform. I suspect this is generally where the problem is originating.

I have dug out my Icom 745, 751 and 761 service manuals. These rigs all use ALC and its time constant to control the output waveform. If you look, every IF and RF amplifier in the transmit chain has a feedback path from ALC. Any time ALC is used in this fashion what you have are non-linear amplifiers, that is, the gain function varies, which will result in intermod products being generated. PSK31 users have known this for a long time. If you see ALC action on a psk31 transmitter, you see intermod products too.

W8JI and W9CF have done a good job analyzing the OUTPUT frequency distribution based upon the rise time of the output but they (and others) then make the logical jump that this also means the output follows the input therefore the rise time of the input is the controlling factor. This logical jump isn't justified without knowing what the transfer function of the transmitter looks like and that it is a linear function. That is, what you put in is what you get out. The ARRL reviews of the CW input/output waveforms conclusively show this is not the case. In math terms:

Input function X Gain transfer function = Output function.

If you don't know the "gain function", you can't know the relationship between the input and output. Therefore, making conclusions about one from the other is not logically correct.

K5MC has shown conclusively that the fourier analysis of the input waveform does show the discreet frequencies in that waveform. Consequently, he has confirmed through the Scientic Method that theory meets results. Yet, there appears to be a wider bandwidth being generated. The logical conclusion is that the transfer function of the transmitter is NOT linear and therefore other intermod products are being generated.

This has the advantage of no one having to say that the analysis (and last 100 years of theory)of the input is wrong or that the analysis of the output is wrong. It simply means no one has arrived at a satisfactory mathemetical description of the transfer function in a typical transmitter.

I will be trying to duplicate K5MC's experiment with function generators. The shaping circuits will be filters, not variable gain amplifiers. I will then run the signal through a linear amplifier to see what comes out. I don't have a spectrum analyzer so I can't use RF darn it.

My guess is that using a simple crystal controlled transmitter with no mixers and only confirmed linear amplifiers will provide a whole different measurement than what Tom has seen with commercial transmitters with multiple variable gain amplifiers and several mixers.

Jim
WA0LYK
 
Bandwidth versus Keying Speed  
by K0RU on June 3, 2007 Mail this to a friend!
You have got to be kidding right? These are engineers? Of what? for what?

Talk about a waste of bandwidth... Duh! read above!

K0RU - Rob
Back to QRQ CW... Where life has a life.
 
Bandwidth versus Keying Speed  
by K5MC on June 3, 2007 Mail this to a friend!
K5MC: AB0WR, W1YW, and SM0AOM, in particular, have really understood the purpose of my article because they are electrical engineers by formal training and experience.

I failed to include WA0LYK in my list above.

WA0LYK: My guess is that using a simple crystal controlled transmitter with no mixers and only confirmed linear amplifiers will provide a whole different measurement than what Tom has seen with commercial transmitters with multiple variable gain amplifiers and several mixers.

Jim, I believe such a rig does have the keying characteristics that I assumed in my simple Fourier series model. I have a variety of rigs myself, including some old Ten-Tecs manufactured 25 to 30 years ago. I'm hoping the HP analyzer I have at school will be adequate to see a discrete line spectrum similar to the Telefunken oscillograms emailed to me by SM0AOM.

BTW, it appears that the arrl.org e-mail domain is down. If anyone would like to see the oscillograms forwarded to me by SM0AOM, you might want to try k5mc@arrl.net rather than k5mc@arrl.org.

73, K5MC
 
Bandwidth versus Keying Speed  
by K5MC on June 3, 2007 Mail this to a friend!
K5MC: I'm hoping the HP analyzer I have at school will be adequate to see a discrete line spectrum similar to the Telefunken oscillograms emailed to me by SM0AOM.

I think the lack of sleep is really starting to catch up with me. I've used the word "oscillograms" several times when what I actually have from SM0AOM are frequency spectrum plots.

73, K5MC
 
RE: Bandwidth versus Keying Speed  
by AB0WR on June 3, 2007 Mail this to a friend!
w9cf:"The Scientific Method requires that a hypothesis be ruled out or modified if its predictions are clearly and repeatedly incompatible with experimental tests. "

The scientific method also requires that a HYPOTHESIS be formulated as the first step.

While I have seen your analysis of the output of a CW transmitter I have yet to see your hypothesis on what the input driving waveform and system transfer function needs to be in order to come up with the spectrum graphs Tom has shown.

Just saying that the output response we see will always be the output response we see because the output response causes the output response just isn't acceptable to me.

With that kind of logic we would not have any knowledge of how things actually work at all.

I suspect that WA0LYK's analysis is correct. It would appear to me that it is confirmed by the fact that many of the CW envelopes seen from CW transmitters actually have an exponential leading and trailing edge. Bandwidth limited square waves do should not have exponential leading and trailing edges.

That would lead me to believe that in many of these transmitters the AM modulation being done in the modulated stage by varying the gain of the system based on the input driving function (i.e. the bandwidth limited square wave) but it is also being varied by an exponential gain transfer function existing in the stage (e.g. an RC low-pass filter being used as a gain control element).

As WA0LYK pointed out this results in a non-linear stage which will generate every conceivable intermod product combination from the frequency elements in the conjoined bandwidth limited square wave thus greatly extending the bandwidth of the transmitted signal.

If this is, in fact, what is causing these CW output responses, which should be much, much narrower than they apparently are, to be extended far beyond theoretical limits there are certainly things that can be done to alleviate this. That is why it is so important to have a firm understanding of both the input driving function as well as the system transfer function. If you just assume the output causes the output you will never be able to make anything any better.

From what I can tell, the 751a keys the an IF oscillator on and off to generate CW. It would be very, very interesting to get an oscilliscope picture of the waveform envelope right after the oscillator and compare it to the transmitter output. I see what I can do to get that. It would help in understanding what is going on.

tim ab0wr
 
RE: Bandwidth versus Keying Speed  
by AB0WR on June 3, 2007 Mail this to a friend!
w8ji:"It’s just totally beyond me why anyone would spend so much energy arguing a point endlessly without making some attempt to confirm it through experiment.

It sounds to me like people want reality to change and conform to what they explain, instead of observing the real world effect and explaining it. That’s not good science. It certainly does not advance the state of the art or help anyone. It is harmful, not helpful. "


Tom,

It is comments like these that make you seem like a total jerk to everyone. It's like a small child complaining that the other kids don't have as many nice toys and saying "why do they want to play with mine?".

Not everyone has $15000 spectrum analyzers sitting in their basements to conduct "experiments" like these. We get by with what we can afford after buying shoes for the kids, paying the car insurance and mortage, and perhaps taking Momma out to supper once in a while.

We depend on others who *DO* have access to the equipment to assist us in learning about this subject we call radio. Whether you like it or not that is just the way the world works.

Whether you remember it or not, Mickey *DID* conduct one of these experiments. Since the results didn't match your worldview you apparently discounted them totally and just blew them out of your mind. And you speak of others wanting reality to change. Heal thyself, physician!

You still seem to be stuck on saying that the output is the output because the output generates the output. You haven't provided a single mathematical model for how the output comes into being. Rise time on an output response is NOT generated by the output response. It is *GENERATED* by the multiplication of a driving function and a transfer response function. When you can offer some insights into what those driving functions and what those transfer response functions might be then I, at least, will be more than happy to look at them and consider them.

Good science attempts to explain the world. It requires *both* hypotheses and experimental results. So far you have only provided the experimental results. W9CF has explained what the output looks like in the frequency domain. Quit complaining about those of us attempting to work out the hypotheses for how this response is generated unless you can contribute something to that piece as well.

If this makes you mad and you want to take your toys and go home, so be it. I found out a long time ago that I'm not indespensible, neither are you. We'll all be sorry to see you go but I doubt anyone will beg you to stay in the conversation.

tim ab0wr

 
RE: Bandwidth versus Keying Speed  
by AB0WR on June 3, 2007 Mail this to a friend!
w8xr:"I've had a couple of comments off-list from folks that are a little intimidated by some of the DSP terms in this discussion and I've shared a more intuitive approach in an article that I've been working on that echos your comments."

Mark,

Some things you may want to consider thinking about so you'll have an answer if someone quizzes you on your writeup.

Your text states that the slope of the frequency determines the bandwidth of the signal (e.g a 50hz sinewave has a steeper slope than a 25hz sinewave).

Yet a cosine wave of 50hz and a cosine wave of 1000000hz neither have any bandwidth at all, their bandwidths are zero.

Because their bandwidths are zero they can't actually have a signaling rate.

A square wave of 50hz and a square wave of 100000hz both have the same slopes with the same absolute bandwidths (their power bandwidths are differ widely) yet their signaling rates are vastly different.

These would seem to be connundrums generated by your explanation.

You might also want to consider something like a raised cosine filter. If you have Filter1 with a bandwidth of T and roll-off of Beta=1 and a Filter2 with a bandwidth of 2T and roll-off of Beta=1 which is the narrower filter and which has the steepest slopes in the time domain?

Another connundrum generated by your explanation.

I think your explanation would help a novice progress in understanding what is going on a lot. But it might also lead that same novice into some bad paradigms if they ever intend to progress on to actually studying the subject at a college level.

Just something to think about.

tim ab0wr
 
Bandwidth versus Keying Speed  
by K5MC on June 3, 2007 Mail this to a friend!
K5MC: In closing, however, I do want to point out that if I have to be subjected to key clicks when operating CW, I would much prefer that the offending transmitter send at a speed of 1 word per 20 minutes rather than 20 words per minute!

The sentence above is the very last one in my article. What was I trying to say here? It was my attempt (apparently, with hindsight, a rather poor one) to vividly illustrate the concepts of AVERAGE power and POWER bandwidth in a simple manner. Let's discuss and compare the two signals above.

In our scenario, the "offending" transmitter is sending at the rate of 20 wpm. For simplicity, let's assume the keying envelope of the CW signal is essentially square wave when we observe it on a decent oscilloscope. Let's assume this transmitter sends a particular message that requires exactly 1 minute of transmission time at 20 wpm.

On the other end, the receiving operator has chosen a filter bandwidth of 250 Hz to copy the 20-wpm message. Unfortunately, the receiving operator misses most of the message because of noise. What can be done to improve this situation?

One approach is to increase the power at the transmitter. But let's assume that that is not an option in this case. Another possible approach is to slow down the rate of transmission! The sending station decides to slow down all the way to 1 word per 20 minutes and, for the sake of discussion, we will assume the receiving operator has plenty of time as well. So the sending operator slows down to 1 word per 20 minutes! (We're talking true proportional spacing here on our code.) Since it took 1 minute to send the message at 20 wpm, it will require 20 minutes to send that same message at 1 word per 20 minutes.

Now what does the receiving operator do before copying this very slow message? He reduces his receiver's bandwidth! He knows that the "essential" or "power" bandwidth o