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. AB0WRHam MemberQRZ Page

You should not see the same waveform above 480hz with a 0.1hz signal as you would with a 100hz signal.

If you are seeing exactly the same waveform then something else is happening.

The high frequency components fall off in amplitude at a (1/n) rate for a square wave.

There is no possible way for the 4801th harmonic (0.1hz times 4801 = 480.1hz) to be as strong as the 5th harmonic (100hz times 5 = 500hz). The 4801th should be down by a factor of 1/4801 (over 70db) from the fundamental. The 5th harmonic is only down by a factor of 1/5 or 14db.

Since the power in the pulse after the high pass filter should be related to the power in each harmonic it passes the total power generated from the 100hz signal should be much higher than the pulse generated from the 0.1hz signal.

Of course the otherconsideration is that if you only have a single pole filter providing a 6db per octave slope you really aren't filtering the low frequency components very well. The harmonics at 240hz will only be down 6db, at 120hz they will be down 12db. That would seem to be enough filtering to see a dfference between a 100hz square wave and a 0.1hz square wave above 480hz, however.

tim ab0wr

2. G3TXQHam MemberQRZ Page

Tim, I think the problem is that you are coming at this from the frequency domain. Just consider it in the time domain for a moment:

If I put just one 0-5v level step into my RC network. I'm bound to get out a single pulse of 5v amplitude with an exponential decay to zero. That's a basic, year 1, lab experiment. If we consider the RC network to be a filter that cuts off everything below 480Hz, there must have been some components above 480 Hz in the input signal, even though it was essentially "0Hz".

The point is that these particular frequency components are a function of the "leading edge" - not of the repetition rate.

If I repeat the above with a step every 1 Second I see exactly the same output waveform, but at 1 second intervals. If I increase the input frequency to 10Hz I see the same again but 10 times as often. It's not until the repetition rate begins to approach the exponential decay time that anything changes - at that point the input frequency is beginning to approach the filter cut-off frequency.

Yes, I know - it makes my head ache, too It may be difficult to explain in the frequency domain, but it's absolutely what happens.

Steve

3. W5DXPHam MemberQRZ Page

This discussion reminds me of the wave/particle duality. If one expects a wave, one will detect a wave. If one expects a particle, one will detect a particle. Could it be that each of you is collapsing the probability wave and detecting what each is expecting?

4. K5MCHam MemberQRZ Page

Steve, your experiment demonstrates the relationship between the rise/fall characteristics and the generation of key clicks in a very vivid manner. The pulses that appear at the output of your highpass filter are, in essence, impulses just as you describe. As you also point out, the amplitude of the impulses is not a function of the keying speed. (Just for the record, I've never argued otherwise.)

However, just in case there are still some folks reading this thread who don't truly appreciate the concept of signal "bandwidth" in its more commonly understood manner in communication systems, let's substitute your highpass filter with a simple lowpass filter with C = 100 nF and R = 640,000 ohms. The 3-dB cutoff frequency of this filter is about 2.5 Hz. Compare the output signal in two different situations:

1. Assume the input signal is a periodic train of square waves (0 to 5 V) with a repetition rate of 2.5 pulses per second (i.e., 2.5 dits per second or 6 wpm).

2. Assume the input signal is a periodic train of square waves (0 to 5 V) with a repetition rate of 25 pulses per second (i.e., 25 dits per second or 60 wpm).

Although there will be some pulse distortion in the first case, the output signal will be much more distorted in the second case. In terms of conveying information, the "essential" bandwidth of the second signal is significantly greater than the first signal and the "occupied/power" bandwidth is a reasonably good measure of that characteristic. (Instead of performing this experiment with actual hardware, I used PSpice.)

Of course, we should use properly shaped pulses rather than rectangular pulses to minimize key clicks. As the FCC discusses in Part 2, the occupied bandwidth (as defined by the FCC/ITU) should be no greater than the "necessary" bandwidth (which varies directly with the keying speed as defined in Part 2). At 60 wpm (50 baud) the necessary bandwidth is 250 Hz (assuming a fading circuit where K = 5) and so the occupied bandwidth (the 99% power bandwidth) should be no greater than 250 Hz; at 6 wpm the necessary bandwidth is 25 Hz (assuming K = 5) and the corresponding occupied bandwidth should be no greater than 25 Hz to insure that the generation of key clicks will not be objectionable on adjacent frequencies.

Since the rise/fall characteristics of traditional CW transmitters are not readily adjustable, there's little doubt in my mind that the occupied bandwidth of many (most) CW rigs is higher than the necessary bandwidth at the slower speeds. For example, my Kenwood 940S (with measured rise/fall times of approximately 5 ms) has a measured occupied bandwidth (99% power bandwidth) of about 190 Hz at 30 wpm, which is quite a bit higher than the necessary bandwidth (125 Hz) specified by the FCC. As I recall, the measured occupied bandwidth of my Ten Tec Orion II at 30 wpm is somewhat less than the necessary bandwidth because I have the rise/fall times set to 8 ms. (Last year I used an Agilent MXA N9020A signal analyzer to measure the occupied bandwidth as a function of keying speed of four different CW rigs that I own.)

73, K5MC

5. G3TXQHam MemberQRZ Page

K5MC: A very helpful summary - I agree everything you've said.

At the risk of making a fool of myself again, I'll try to summarise what I have personally learned from this monster thread. Although this is a qualitative summary, I believe it is consistent with all the experimental observations I have made, and the mathematical analyses I have read. I'll use my squarewave / RC high-pass filter experiment as as a "vehicle", and by high-order sidebands I will mean the frequencies above 480Hz passed by my filter.

When I lower the squarewave frequency (reduce the keying rate) from 10Hz to 5Hz:

1) There is a smaller proportion of the total power in the high-order sidebands - in fact it has halved. [RC filter experiments]

2) Therefore the bandwidth must have decreased, because the band of frequencies which encompass 99% of the total power must have decreased.

3) The shape of the power spectrum envelope looks almost identical, but the sidebands will now be spaced by 5Hz instead of 10Hz, and there will be more power at the centre of the spectrum. The reason that the envelope shape appears identical away from centre is that it is determined by the risetime of the square wave, and that did not change. [Figure 4 at http://fermi.la.asu.edu/w9cf/articles/click/click.html#f2]

4) Despite the near-identical shapes of the power spectrum envelopes, the bandwidth is narrower. Had W9CF "normalised" his two spectra for the same average power, his "50mS" waveform would sit several dB lower than his "20mS" waveform; it would then be much more obvious that the bandwidth had reduced and that the power in the high-order sidebands was lower.

5) The high-order sidebands have been halved in power and are spaced more closely, but they have the same amplitudes relative to one another and the same phase relationships. They exist throughout the keying period (assuming the keying waveform is periodic). Somewhat surprisingly, the combined effect of these high-order sidebands is to produce an impulse that has the same amplitude and width, despite the sidebands containing only half the power. The reduction in power is fully explained by the halving of the pulse repetition rate. [ RC filter experiments and http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=17.0 ]

I guess I'm simply now agreeing with everything that you have been saying - it's just taken me a while to get there

I'll say again that what "threw me" (and others I'll bet) is the ITT/FCC definition of bandwidth which allows a narrower-band signal to produce adjacent channel key clicks at the same amplitude as a wider-band signal.

73,
Steve

6. K5MCHam MemberQRZ Page

Steve, I appreciate all of your comments in this discussion on bandwidth. There's little doubt in my mind that you and I are very much in agreement here.

It was obvious to me early on in this discussion that you have a solid background in signal analysis/communications. I can imagine it was a thrill to meet Viterbi in person as you mentioned. Although my graduate education focused primarily on electric power engineering, in my spare time over the past few years I have been trying to learn more of the detailed mathematics of information theory and related topics (error detection and correction, etc.) in communications. Maybe one of these days I will have the opportunity to teach such a course at my school!

73, K5MC

7. G3TXQHam MemberQRZ Page

Mickey, what really "gripped me" as a youngster in those days was the "magic" of forward-error-correcting coding which allowed us to drop power levels by 3dB (speech) and 5dB (data) and achieve exactly the same information error rates. At the time the UK did not have its own satellites and we were "renting" channels on US satellites. We were charged "by the Watt" because power is the precious commodity on the satellite. Suddenly, by introducing FEC we were able to more than halve our costs; moreover, only modest equipment changes were needed at the base stations, and none in the spacecraft - avoiding my having to travel 24,000 miles into space and back

Thanks for the discussions - they have been enjoyable and educational.

73,
Steve

8. AB0WRHam MemberQRZ Page

Steve,

I'm sorry this is so late. I've been away for a while.

The Fourier transform of a unit step is the impulse function plus a term that falls off at a rate of (1/w).

That is exactly the same rate that the components of a square wave fall off.

As the step function becomes "less" of a step the steeper the fall off becomes -- e.g. 1/w^2 to 1/w^3.

Is this what you are trying to get at here?

tim ab0wr

9. G3TXQHam MemberQRZ Page

Tim, I was trying to respond to your earlier statement:
by showing that I do see the same waveform even when the signal is lower than 0.1Hz - i.e. a single step function.

This was "Point 5" in my earlier posting where I tried to wrap things up.

73,
Steve

10. AB0WRHam MemberQRZ Page

I'm still not sure I understand why you are seeing the same waveform. If you have an exponential output from your filter the amplitude of the spectral components should fall off at a rate of 1/(w^3), at least as I understand it. (I need to go back and check the math on this) That means the 200hz component should be down 55db and the component at 500hz should be down over 63db.

This so-called "keyclick" bandwidth generated by a step function with an exponential rise-time falls off much faster than the bandwidth generated by a recurring waveform which only falls off as at a rate of 1/n where n is the number of the harmonic.

I would expect, therefore, to see your high-pass filter waveform dominated by the spectral components of the recurring waveform above a certain speed.

E.g. the 1500th harmonic of a square wave should be at the same level as the exponential "key-click" bandwidth at 500hz (1/1500 for the harmonic and 1/1500 for the w^3 term of the step function). Thus, for an "equal" contribution to the waveform, that means that 1500f = 500hz so f = .33hz.

So I would expect the high pass waveform from any keying rate over .33hz to begin to be dominated by the spectral components from the recurring waveform. At 10hz, more than an order of magnitude from 0.33hz, there should be a significant difference in the waveforms you see.

The impulse that you see is of *far*, far more interest to me. It is this kind of a waveform that can generate all kinds of intermodulation products and distortions from later amplifier chains with non-linearities. Any transmitter with capacitive coupling anywhere in the circuit chain associated with keying could cause big problems. It would be this kind of implementation specific detail that would fit with why you see bad key clicks from some transmitters and not from others. It could also explain why you sometimes see a "click" on the some elements and not on others.

tim ab0wr