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Author Topic: For W8JI: key clicks and amplifier non linearity  (Read 64709 times)
G3TXQ
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Posts: 1845




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« Reply #360 on: September 09, 2015, 11:42:55 AM »

At this point, I'm not even sure where we stand, so I'll just stick with SDR engineering.

OK - I'm going to summarise my position and then call it a day. Please note that everything which follows relates to a periodic signal such as repetitive Dots, and an analysis window of one or more of those periods:

1) The whole basis of Fourier analysis is that this signal can be represented by a set of sinusoids which are constant amplitude throughout the analysis period.

2) The mathematical time-domain expression for that periodic signal contains terms which represent the spectral components, and they are time invariant

3) If we key a carrier on and off quickly enough that we can examine individual spectral components with practical filters, we observe that they are constant amplitude.

4) There is no requirement for the instantaneous power in the time-domain signal to be equal to the instantaneous power in the spectral components - we saw that in the simple example of an AM sine-wave modulated carrier. So there is no anomaly in having power in the spectral components when the modulated carrier is Off. All that is required is that the total energy in the spectral components should equal the total energy in the modulated carrier when integrated across the analysis period.

5) At typical keying speeds and with practical bandwidths we don't observe individual spectral components, but rather an aggregation of many of them. That aggregation results in the energy in the spectral components being concentrated into a small time period around the keying transitions - which we observe as keyclicks.

6) If we define "sidebands" to mean an aggregation of many spectral components, then sidebands only exist at the transitions and not between the Dots; if we define "sidebands" to mean individual spectral components, then they exist during and between the Dots.

Steve G3TXQ
« Last Edit: September 09, 2015, 11:47:41 AM by G3TXQ » Logged
AC7ZN
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« Reply #361 on: September 10, 2015, 03:04:48 AM »

I appreciate Steve's summary.  It would be presumptuous for me to summarize my take on things since I have not been an active participant here, so let me start with a summary of what the Fourier integral does.  We will need to use the Fourier integral to add insight to what is happening because one of my claims is that a CW spectrum cannot be adequately addressed by periodic analysis.

Those of you who understand and have worked with the discreet Fourier transform (DFT, or FFT) will have no trouble extending those concepts to the Fourier integral.  In the DFT we know that increasing the sample rate (using more sample points in our set) also increases the frequency resolution in the frequency domain (there are more frequencies, more closely spaced).  Lengthening the dataset in time increases the period (makes the repetition rate slower) and potentially adds lower frequency energy to the spectrum.

Now imagine increasing the both the number of samples and the time length of the dataset  to infinity.  This is the Fourier integral.  Because the time of the dataset is infinite, the period is infinite and becomes nonperiodic, since the one dataset covers all time.  Both the time domain and frequency domain have infinite resolution and are continuous, not discrete.  We still multiply all datapoints by the sine and cosine of every frequency as is done in the DFT, but we now do it analytically with calculus.  As with other calculus functions, we can often successfully approximate results with discreet computer calculations by making sure we include enough of them to give accuracy, and the DFT (FFT) can be used to do this by simply increasing sample rate and period until meaningfully accurate results are obtained.

Some common results have been tabulated.  We know the Fourier transform of a Dirac delta function is 1 at all frequencies.  Its dual, a Dirac delta function in the frequency domain is 1 for all time. A Dirac delta function is a mathematically convenient construct that has infinite amplitude, zero width and integrates to one.  On plots it is noted by an arrow pointing up. It can also be called an impulse, and the impulse response of a filter assumes this function has been applied to the input.

The unit step is of particular interest in CW, because the (clicky) CW tone can be modeled as a pulse consisting of the convolution of unit steps with the carrier.  The unit step spectrum has a Dirac delta function at zero, then a spectrum of 1/jw. We will plot this and comment on it in a future post, hopefully.

73,
Glenn AC7ZN





 


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G3TXQ
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« Reply #362 on: September 10, 2015, 06:58:59 AM »

Glenn,

I appreciate your input.

I agree with all that you have said, although I wonder where the third sentence is taking us -  Fourier analysis of an aperiodic 3 minute CW QSO may test my abilities  Wink

Steve G3TXQ
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REASTON
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« Reply #363 on: September 10, 2015, 07:27:38 AM »

This whole thread just cracks me up.  Lots of talk about math, but I still don't see any.  How can you people "talk" about math.  You either know it and write it or you don't know it.  All this crap in this thread is everybody blowing smoke trying to convince each other they are RF Engineers when they are not.
« Last Edit: September 10, 2015, 09:11:36 AM by REASTON » Logged
W1BR
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« Reply #364 on: September 10, 2015, 08:42:36 AM »


I would summarise things like this:

 
2) At typical keying speeds, and with practical receiver bandwidths, we never hear individual spectral components but an aggregation of many of them. The summation of those many components is a signal that is impulsive, with peaks coincident with the OOK transitions.

 
Steve G3TXQ



Isn't that basically what W8JI was trying to convey before this topic became an advanced math discussion?
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G3TXQ
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« Reply #365 on: September 10, 2015, 09:29:11 AM »

Isn't that basically what W8JI was trying to convey before this topic became an advanced math discussion?

I don't know - I wasn't part of the early discussions so I don't know what W8JI meant.

I did say way back in #250:

"If by "sidebands" you mean a summation of several individual spectral components, then I agree they are not continuous; but if we are talking about separate spectral components, then they are continuous."

But then in #285 W6RZ challenged our claim that the spectral components were continuous; maybe he meant to say "sidebands", but the term he used was "spectral tones".

Steve G3TXQ
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W6RZ
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« Reply #366 on: September 10, 2015, 09:35:36 AM »

What are "spectral components"?
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G3TXQ
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« Reply #367 on: September 10, 2015, 09:48:30 AM »

What are "spectral components"?
The individual, frequency-domain, spectral lines resulting from a DFT.

What did you mean by "spectral tones"?

Steve G3TXQ
« Last Edit: September 10, 2015, 09:51:23 AM by G3TXQ » Logged
G3TXQ
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Posts: 1845




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« Reply #368 on: September 10, 2015, 09:49:22 AM »

This whole thread just cracks me up.  Lots of talk about math, but I still don't see any.  How can you people "talk" about math.  You either know it and write it or you don't know it.  All this crap in this thread is everybody blowing smoke trying to convince each other they are RF Engineers when they are not.
Perhaps you missed these: #290, #309,#322

Steve G3TXQ
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W6RZ
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Posts: 365




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« Reply #369 on: September 10, 2015, 10:01:57 AM »

What are "spectral components"?
The individual, frequency-domain, spectral lines resulting from a DFT.

What did you mean by "spectral tones"?

Steve G3TXQ

The same thing. We just disagree on exactly when they exist. And by "exist", I mean in the real world, transferring power. Not just as a mathematical construct.

BTW, I'm not an RF engineer. I'm a software engineer with an EE background. The last 18 years of my professional career were in the video compression industry working on MPEG-2 encoders and systems. Before that, military data communications networks.

That's why I'm having so much fun with SDR. What a wonderful marriage of my professional skills and my lifelong hobby, amateur radio.
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G3TXQ
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Posts: 1845




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« Reply #370 on: September 10, 2015, 10:39:38 AM »

The same thing. We just disagree on exactly when they exist. And by "exist", I mean in the real world, transferring power. Not just as a mathematical construct.

Understood - but I would point you back to a couple of examples we discussed earlier, to think about whether they are just a mathematical construct: we can extract "real" energy from a spectral component at the output of a switching mixer, even when the switch is Open; we can extract "real" energy from the spectral components of a sine-wave modulated AM signal, even through the trough where the instantaneous power in that modulated signal is zero. But it seems that folk find it difficult to accept once the modulating frequency gets low.

I can understand your fascination with this stuff. My background was RF engineering with the BBC, but then I worked on developing the convolutional error correction coding systems for the UK's military ComSat programme. That really grabbed my interest, and still does; the highlight was meeting Andrew Viterbi!

Steve G3TXQ
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K9AXN
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« Reply #371 on: September 10, 2015, 11:24:42 AM »

Steve,

In #306 you have a photo containing two wave forms.  You say the top is of a carrier running through a diode switch and the lower is of the keyed signal passed through a filter selecting the carrier frequency.  The carrier is present in the gaps between key down time.  What you did is place the channel 2 probe on the input to the diode switch and of course the carrier is present, it has not been switched off.

If you review #309 and the common modulation formula that you presented, you will see that when the key is closed modulation commences generation side bands until the end of rise time where the side bands cease.  Now, with the key remaining closed, only carrier is present.  When the key is opened, modulation reoccurs during the quench time, again generating side bands.  Then there is nothing in the inter-key gaps.

There is a problem with 306 and the narrative.

Kindest regards Jim
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W6RZ
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« Reply #372 on: September 10, 2015, 12:17:56 PM »

I can understand your fascination with this stuff. My background was RF engineering with the BBC, but then I worked on developing the convolutional error correction coding systems for the UK's military ComSat programme. That really grabbed my interest, and still does; the highlight was meeting Andrew Viterbi!

Steve G3TXQ

Then you would absolutely love the SDR based DVB-T2 transmitter I developed over the winter. With this GNU Radio flow, you can transmit a signal exactly like the HD multiplex you receive from Crystal Palace (or wherever your regional DVB-T2 transmitter is located and assuming you actually watch TV).

The BBC was instrumental in promoting DVB-T2 technology, and I used their reference streams to verify my software. Another interesting aspect is the error correction coding technology. Instead of Viterbi codes, DVB-T2 uses a code called Low-Density Parity-Check or LDPC. The interesting part is that LDPC coding was invented in 1960 by Robert G. Gallager. Because computers were not powerful enough in 1960 to implement the codes, it was forgotten for many years. Then it was rediscovered in 1996 and was specified in DVB-T2 instead of the then popular Turbo codes.

Also, I collaborate with one of your countrymen, Charles Brain G4GUO. Charles is leading the charge for digital amateur TV or DATV with his transmitter project DATV-Express.

http://www.datv-express.com/

He also has a very nice blog at:

http://g4guo.blogspot.com/

Here's the graph with the exact BBC DVB-T2 parameters that delivers 40.2 Mbps is an 8 MHz channel. Just a little more complex than the previous ones I've posted.

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G3TXQ
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« Reply #373 on: September 10, 2015, 12:32:55 PM »

In #306 you have a photo containing two wave forms.  You say the top is of a carrier running through a diode switch and the lower is of the keyed signal passed through a filter selecting the carrier frequency.  The carrier is present in the gaps between key down time.  What you did is place the channel 2 probe on the input to the diode switch and of course the carrier is present, it has not been switched off.

Of course not - the upper trace is the output of the diode switch; the lower trace is the output of the filter selecting the carrier.

That's the fundamental point - the carrier spectral component is present even when the switch is off. Its power is real - not just a mathematical construct. If the carrier frequency was 5MHz and the switching frequency was 1MHz we'd have continuous energy available at 5MHz, 4MHz and 6MHz, not just when the switch was On.

I really don't know how much plainer to put it.

If you review #309 and the common modulation formula that you presented, you will see that when the key is closed modulation commences generation side bands until the end of rise time where the side bands cease.  Now, with the key remaining closed, only carrier is present.  When the key is opened, modulation reoccurs during the quench time, again generating side bands.  Then there is nothing in the inter-key gaps.

Nope - when you expand it, that formula contains a first term of 0.5xAcxsin(ωct). That's a sine wave whose amplitude is 0.5xAc. Notice that the amplitude is not time varying - it's a constant. And that's exactly what the photo in #306 shows.

As I keep trying to explain, there is a temporal redistribution of energy between the time-domain and frequency-domain representations. The total energy is the same in each case, but in the time domain it is all contained in the first half-cycle of the modulation, whereas in the spectral components it is evenly distributed across the whole modulation cycle.

If you have trouble with that concept, just go back to the basic sine-wave AM case. We know the carrier component and the sideband components are constant amplitude throughout the modulation cycle, even though the modulated wave has many times more energy in the first half-cycle compared to the second half-cycle.

Steve G3TXQ
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G3TXQ
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« Reply #374 on: September 10, 2015, 12:42:46 PM »

The BBC was instrumental in promoting DVB-T2 technology, and I used their reference streams to verify my software.

Interesting stuff!

I paid a visit to the BBC's Research Department during my training with them back in 1965. We were very excited when told we were going to be shown the newly-developed Line Standards Converter which converted US 525-line TV pictures to our 625-line. We wondered what amazing new digital technology were going to see.

Imagine our disappointment when we saw a UK 625-line camera pointing at a US 525-line monitor! The "high-tech" bit was that the monitor had been modified to incorporate "spot wobble". In other words the resolution was deliberately degraded so that there was no strobing between the two line structures.

Happy days!

Steve G3TXQ
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