Comb spectrum generation
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wakibaki
Banned

Join Date: Jan 2008
Quote:
 Originally posted by bwaslo Or you can subtract a sinewave that is 2/pi in amplitude from the square wave twice.
Ah, right, yeah, forgot about the scaling factor.. I'll redo that in the morning.

I'll think about the even harmonics. That's the odd ones and the fundamental sorted.

w

 7th July 2008, 08:35 AM #12 Elvee   diyAudio Member     Join Date: Sep 2006 Thanks for your contributions, but I want to generate a binary sequence, not a succession of digital words. And I would preferably like to use some form of theoretical reasoning. I'll take an example: I want a spectrum similar to that of a Dirac pulse, thus I start with a short pulse having a repetition rate of 1KHz. The pulse has to be short enough to obtain a flat spectrum up to the 10th or 20th order; this is no problem. The problem is to remove the fundamental; I can do that by adding an identical pulse having a 180° shift. If I use an identical pulse however, I will remove not only the fundamental, but also all odd-ordered harmonics. This means that the added pulse must have the same fundamental contents, but also a spectrum that adds energy to the existing harmonics, to keep the spectrum flat. This can be done by splitting the pulse into two shorter pulses, symetrical about the 180° mark: see picture. There is still a fundamental leakage, but this is no real problem: I could fine-tune the small pulses to remove it completely. What is more troublesome is the disturbance to the amplitude of the harmonics: they are all present, but not equal anymore, and trying to fix it by trial and error seems an impossible task: if I "repair" one part of the spectrum, I'll damage another. So I would like to take my reasoning further and find a clever, deterministic way to place additional transitions at the right instants, but at the moment, that's where I'm stuck.
Elvee
diyAudio Member

Join Date: Sep 2006
I have had problems with the picture. Here it is:

Doesn't work. I'll retry later.
Attached Images
 comb.jpg (92.0 KB, 70 views)

Elvee
diyAudio Member

Join Date: Sep 2006
One more tentative:
Attached Images
 comb.jpg (20.8 KB, 80 views)

 7th July 2008, 11:15 AM #15 wakibaki   Banned   Join Date: Jan 2008 What do you want this signal for? To generate 44k1 16-bit conventional PWM requires a clock speed approaching 3GHz. The highest frequency that can be accommodated is ~22k. Magic sinewaves are a variation of PWM which is really effective with signals << slower than the sample rate. e.g. 4MHz is a good clock rate for a 60Hz sinewave. Perhaps if you tell us what actual frequencies and sampling frequencies and resolution you are talking about, we might have a better idea what is going on... w
 7th July 2008, 02:39 PM #16 bwaslo   diyAudio Member     Join Date: May 2006 Location: Portland, Oregon! Maybe first generate the steady-sampled sequence of digital words (relatively easy, as described above), and then convert that to a Pulse width modulated signal so that it is a binary sequence? I'm assuming your binary sequence is allowed to have fine resolution for the timing of the edges (and isn't constrained to particular sample times)
wakibaki
Banned

Join Date: Jan 2008
Quote:
 Originally posted by Elvee The problem is to remove the fundamental; I can do that by adding an identical pulse having a 180° shift.
Doesn't that just result in 2 pulses where you only had one before and a repetition rate of 2kHz?

That's why the fundamental disappears... and all the odd ordered harmonics. You're now looking at the harmonics of a 2k signal.

w

puh-leeze!

Elvee
diyAudio Member

Join Date: Sep 2006
Quote:
 Originally posted by wakibaki Doesn't that just result in 2 pulses where you only had one before and a repetition rate of 2kHz? That's why the fundamental disappears... and all the odd ordered harmonics. You're now looking at the harmonics of a 2k signal.
Yes, exactly, and that's the reason why the additional pulse is split into two narrower pulses, as you can see on the sim (sorry for the quality, that's all the forum would accept). This leaves the odd ordered harmonics, but the amplitudes are not correct, because I picked the pulses width and timing more or less randomly.
I need the signal for audio signals processing, this means that ideally, I would like a (suppressed) fundamental between 100Hz and 10KHz, but I'd be happy with just 1KHz to begin with.
I can content myself with just the 10 first harmonics; what happens further is of no concern.
The tolerance on the amplitudes needs not be very strict: +/-1dB is OK. This means the timing accuracy can be very much relaxed compared to magic sinewaves: +/1dB accuracy translates into approx 14dB rejection for magic sinewaves, which isn't very stringent. I estimate the granularity of the timing has to be something like 20X the highest frequency to be generated. The last harmonic of the highest frequency being 100KHz, this sets the basic clock at 2MHz.
One thing is important however, it is the rejection of the fundamental. But once I have more or less the spectrum I'm looking for, I can easily tweak one of the pulse width by 1 or 2ns to get a perfect rejection, without upsetting significantly the amplitudes of the harmonics.

 8th July 2008, 09:37 AM #19 wakibaki   Banned   Join Date: Jan 2008 The waveform you require and its derivation will be no less complicated than the one derived by summing the components and converting to PWM. In fact if the conversion is perfect, the result will be identical. You are chasing a chimera. w
Elvee
diyAudio Member

Join Date: Sep 2006
Quote:
 Originally posted by wakibaki The waveform you require and its derivation will be no less complicated than the one derived by summing the components and converting to PWM. In fact if the conversion is perfect, the result will be identical. You are chasing a chimera. w
I don't think so.
The waveform shown in the sim is not overly complicated, and yet it nearly fits the bill. I could easily improve it by a trial and error method, but I find it preferable to use a direct, mathematical method. If I have no other choice however, I will revert to the blind method.

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