HF Digital Error correcting? Also, what's up with PSK31?

Discussion in 'General Technical Questions and Answers' started by N0NS, Oct 9, 2008.

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  1. G3TXQ

    G3TXQ Ham Member QRZ Page

    Mike, one other example which may help, particularly if you are still wondering how the high-order sidebands which determine the shape of the leading edge "endure" beyond the edge.

    Take one cycle of a very low frequency squarewave - let's say it's on for 5 seconds and off for 5 seconds i.e. 0.1Hz. Let's suppose the rise-time is sufficiently short that there have to be significant sidebands up to around 1KHz. I guess the question is - does that 1KHz sideband exist for the full 10 seconds?

    To try to convince you that it does - in engineering terms rather than maths - let's perform the spectral analysis by submitting the squarewave to a bank of filters. We will need many filters whose centre frequencies are spaced by 0.1Hz because that is the sideband spacing. And here's the nub of the argument: the bandwidth of these filters will need to be a very narrow 0.1Hz.

    Now apply the leading edge of the squarewave to the bank of filters. What do you think you will see at the output of the filter centred on 1 KHz? The answer of course is a 1KHz sine wave that continues for the full 10 seconds - that's how long a 0.1Hz bandwidth filter will "ring".

    Hope that helps rather than hinders.

    And Mike, for the most convincing demonstration, go to:

    Set all the sin wave sliders to zero. Then drag the 15f slider to 0.235. Then drag the 13f slider to 0.323. Progressivley add sidebands as follows:
    15f=0.235, 13f=0.323, 11f=0.382, 9f=0.426, 7f=0.352, 5f=0.323, 3f=0.205.

    Notice that there is no fundamental or second harmonic, but we've generated an impulse at twice the fundamental frequency followed by pretty much nothing, even though the higher order sidebands up to 15f are there all the time.

    Last edited: Oct 28, 2008
  2. W5DXP

    W5DXP Ham Member QRZ Page

    What's the difference between stopping modulating with a square wave and merely changing frequencies from 1 kHz to 1 yoctoHz?
  3. AB0WR

    AB0WR Ham Member QRZ Page

    I think Mike believes the harmonics are there all the time during the signal.

    I think his point is that we can confirm that the fundamental is there by inspection if nothing else.

    If the fundamental is there for the whole time, then inductive logic would dictate that the harmonics are as well.

    tim ab0wr
  4. G3TXQ

    G3TXQ Ham Member QRZ Page

    Not much - but I'm still building my filter with a yoctoHz bandwidth, so at the moment I'm finding it difficult to discriminate the yoctoHz sidebands. But I'm getting there - I just got to wind a couple more T-68-2 toroids and I'll be finished :)

  5. W5DXP

    W5DXP Ham Member QRZ Page

    :) I guess the serious question is: How do the sidebands know if the modulation has stopped thus requiring the sidebands to cease to exist vs the frequency merely being changed to a much lower frequency thus requiring the sidebands to continue to exist?
  6. G3TXQ

    G3TXQ Ham Member QRZ Page

    Cecil, I hesitate to try to answer your conundrum because I suspect it will just set the debate back a few hundred postings, and I'm not claiming I have all the answers. But let me have a try at a very "qualititative" answer based in the "engineering world", rather than in the "maths world" where the answer is conceptually more easy.

    Let's say we have a 10Hz modulating squarewave which changes frequency to a 1Hz modulating squarewave. I believe you are asking how the sidebands which are present during the period of 10Hz modulation know "what to do" during the first "part cycle" when the modulation changes to 1Hz.

    The sidebands you are asking about are spaced by 1Hz and so can only be discriminated by a bank of 1Hz bandwidth filters. Those filters will "ring" for something like 1 second when excited by a step function. So, for as long as the 1Hz modulation is present there will continue to be an output despite the change in frequency. Once there ceases to be a transition at the "expected" 0.5 second interval, the sideband will cease to exist.

    If you now postulate that the frequency change might have been from 10Hz to 100mHz instead, I simply argue that the sidebands you are enquiring about would need a 100mHz filter to discriminate and they would have a "ringing period" of 10 seconds etc etc etc.

    Conceptually this conundrum seems to me to be the obverse of what happens at the beginning of a modulation cycle. If we take a 1MHz carrier and AM modulate it with a 1KHz sine wave we will produce sidebands at 1.001MHz and 0.999MHz. Now, tell me if those sidebands existed 100 uSec after the start of the modulation sine wave? If not, after what time did they appear? And if they did appear instantly, how did they "know" at that stage that the modulation envelope was going to be a 1KHz sine wave and that they were "required to be" 1.001MHz and 0.999MHz?

    Don't you just love this stuff :)

  7. K5MC

    K5MC Ham Member QRZ Page

    Cecil, to find the (classical) Fourier transform of a (single) time-limited pulse one must know what the complete pulse “looks like” in the time domain. You can’t determine the Fourier transform of a pulse that lasts for 5 ms after only observing the first 1 ms of the pulse. Therefore, you also can’t determine the “bandwidth” of the pulse (in a classical sense) until the entire pulse has been observed.

    For example, a rectangular pulse lasting 1 ms has a different Fourier transform (and a different “essential” bandwidth) than a rectangular pulse lasting 2 ms. (In fact, the 1-ms rectangular pulse has twice the essential bandwidth as the 2-ms rectangular pulse according to Fourier analysis.)

    As I believe I did last year in my eHam articles, I will quote from a journal paper that a graduate student and I wrote over 10 years ago:

    The basis functions used in Fourier analysis, sine waves and cosine 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. Thus, if there is a local transient over some small interval of time in the lifetime of the signal, the transient will contribute to the Fourier transform but its location on the time axis will be lost. Although the short-time Fourier transform (STFT) overcomes the time location problem to a large extent, it does not provide multiple resolution in time and frequency, which is an important characteristic for analyzing transient signals containing both high and low frequency components. (From “Discrete Wavelet Analysis of Power System Transients” published in the November 1996 IEEE Transactions on Power Systems)

    According to classical Fourier analysis, the keying sidebands do not suddenly disappear between the individual dits or in the middle of each dit when sending dits at 60 wpm, 30 wpm, or even 2.4 wpm (corresponding to 25 dits per second, 12.5 dits per second, and 1 dit per second, respectively). Since we are assuming a periodic signal in this case, the Fourier series is the obvious math model to use here rather than the Fourier transform.

    If one wants to use the short-time Fourier transform to examine the spectrum only during the rise time (or fall time) of one pulse, that spectrum will look quite different than the spectrum over the entire duration (or period) of that pulse. However, the spectra of two pulses that have identical rise shapes/times but different pulse durations will be identical if the short-time Fourier transform is used only over the rise time of the two pulses.

    73, K5MC
  8. W5DXP

    W5DXP Ham Member QRZ Page

    If, as we do, the sidebands waited to see what the present complete pulse "looks like", they wouldn't be correct in the past. Yet, if the sidebands are wrong about what the future complete pulse is going to "look like", they wouldn't be correct in the present. Seems like those sidebands are smarter than I am.:)
  9. G3TXQ

    G3TXQ Ham Member QRZ Page

    CW Keying bandwidth


    Thanks for drawing attention to your eHam article. I spent much of yesterday evening reading it and the many ensuing postings. Perhaps, as a "new boy" to these forums I might be allowed some observations. I apologies if these "angles" have already been covered - I can't pretend that I read every one of the eHam postings in detail. And I have no intention to re-open the debate - merely to offer a few thoughts.

    1. The "problem"

    It seemed to me that much of the debate ensuing from the eHam article was an attempt to reconcile your mathematical analysis what what folk observe in practice.

    I have the same dilemma. I have no reason to question your analysis, which demonstrates clearly that keying speed affects bandwidth. On the other hand, when I listen on my receiver to key clicks in an adjacent channel, their amplitude is independent of keying speed - I did the measurements this morning. How can these two things co-exist?

    2. Observations

    In trying to grapple with these apparently conflicting facts, I revisited my very simple experiments with an RC high-pass filter driven from a function generator. It seems to me that what I observe at the output of this very simple filter on an oscilloscope is representative of the energy contained in the "high order sidebands".

    I apply a 0-5v square-wave with a very short risetime and observe the amplitude of the output signal as I vary its frequency. I observe no change in the output pulse amplitude or shape, and so I must conclude that the power in the "high order sidebands" did not vary with keying speed.

    I now apply a 0-5v square-wave with longer rise and fall times. I note a drop in the amplitude and shape of the output signal, but again, it does not change as I vary the "keying rate".

    It seems to me that this simple experiment with a resistor and capacitor confirms what I measured on my receiver.

    3. Trying to resolve the dilemma

    How can these observations be reconciled with the conclusion in your eHam paper that the bandwidth increases with keying speed? I believe that the answer may lie in how "bandwidth" is defined.

    Your analysis defined bandwidth as the "frequency band in which 99% of the total average power resides". So, if my RC experimental conclusions are correct, that a particular set of sidebands contain the same power whatever the keying speed, a change in bandwidth can only be explained by a change in average power during my experiment.

    That led me to look again at the keying input to my RC filter. Is it possible that the average power of the square-wave changes with frequency?

    Well, yes it is. Take the case where the square wave had the slower rise and fall time and it becomes obvious that the total "area under the curve" reduces as the frequency increases and the rise and fall times become a more significant fraction of the mark/space time.

    Once we recognize that (for non-zero rise and fall times) an increase in keying speed causes a decrease average power, it becomes clear that the constant power in the sidebands will be interpreted as an increase in bandwidth by the earlier definition.

    It seems to me that my rather poor, qualitative, analysis would account for your analytical results. It would predict little change in bandwidth with keying speed for an ideal square wave (because the average power remains constant), and progressively more change in bandwidth with keying speed for "softer" waveforms.

    It also seems that the gradient of the sideband envelope at the point where 90% of the power is contained would mean that small changes in power level equate to large differences in bandwidth.

    4. Is there a "better" definition for bandwidth

    If we accept for a moment that this definition of bandwidth is "unhelpful" in explaining real-life observations of CW signals (even though it is used in international standards), it begs the question "is there another definition that 'does better'"?

    Going back to my earlier RC filter experiments, it's clear that the change in bandwidth was caused because the average power changed with keying speed. However, what was constant in my experiment (which led to the sidebands containing constant power) was the amplitude of the keying waveform - akin to the Peak Envelope Power.

    That leads me to wonder whether a definition of bandwidth based on PEP, for example "the frequency band in which the average sideband power represents 90% of the peak Envelope Power", might be more helpful; for CW signals at least. It seems to me it should certainly lead to bandwidths which are less dependent on keying speed.

    And this seems more representative of the "real-world" situation; when we change keying speed we don't adjust drive level to maintain the same average power - we maintain the same peak power.

    I don't have the maths to check it, but I would be very interested to see whether re-working your Fourier coefficients against a PEP-based definition of bandwidth shows significantly less dependence on keying speed.

    As an aside, I have been interested to see how similar the overlaid spectra are for different keying speeds in the work of W9CF and KE3HO; what differences there are seem to be entirely within the central peak of the spectra. I'm left with the "gut feeling" (no more) that the subtle changes in average power caused by varying the keying speed, which I have been trying to describe in time-domain terms, must somehow be related to that central peak in the spectrum.

    Once again, apologies if this is all "old hat", but it has all been new to me :)

  10. G3TXQ

    G3TXQ Ham Member QRZ Page


    I just realise what a "load of rubbish" I just posted - I've left it in place in case at least some of the thought processes are helpful to others.

    For starters, I realised I mis-read your Table 1, mixing up the rows with the columns!


    Clearly, if the amplitude and shape are the same the power in the high-order sidebands is proportional to the keying speed!!

    So, is one explanation of the apparent conundrum that the bandwidth does indeed increase with keying speed, but that subjectively we fail to perceive the increased power in the sidebands because it appears as the same impulsive wave shape but at a higher repetition rate?

    Back to the drawing board and another coffee :)

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