Is it possible to generate harmonic distortion analytically?
in [DSP]
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From: Jerry Avins on 8 Mar 2010 00:17 Jerry Avins wrote: ... > I don't know of a comprehensive treatment. ... People who try to build semiconductor amplifiers that sound like tube amplifiers dig deeply into controlled distortion. That avenue might provide some leads. Jerry -- It matters little to a goat whether it be dedicated to God or consigned to Azazel. The critical turning was having been chosen to participate. �����������������������������������������������������������������������
From: Les Cargill on 8 Mar 2010 16:34 robert bristow-johnson wrote: > On Mar 7, 6:06 pm, Les Cargill <lcargil...(a)comcast.net> wrote: >> Richard Owlett wrote: >>> Les Cargill wrote: >>>> Jerry Avins wrote: >>>>> Les Cargill wrote: >>>>>> (in PCM streams, of course) >>>>>> What is a good book or website which can expose techniques which might >>>>>> be of use to do this? >>>>>> Thanks in advance. >>>>> The question as I understand it is so simple that I believe I may not >>>>> really understand it. >>>> That is one of the most beautiful heuristics of human communication, >>>> stated in a very good sentence. I am sorry; I don't know enough to know >>>> whether I asked the question properly. >>> He does do that well, doesn't he ;) >>>>> Assuming that I do, the answer is "Of Course." To show that, operate >>>>> on the samples with any non-linear function. >>>> Randomly, or with malice and forethought? Which particular nonlinear >>>> functions would specifically produce second, third or fifth >>>> order harmonic distortion? >>> Not sure of your goal. >>> A simple minded brute force method that *think MAY* meet your criteria >>> _MIGHT_ be: >>> 1. perform DFT >>> 2. for each harmonic "q", multiply the value in bin n by r(q,n), >>> and add it to the value in bin q*n. >>> 3. perform IDFT (and NO, I don't know how to VALIDLY handle the >>> fact that you have now increased the number of bins by the >>> highest harmonic created ;/) >>> { above presumes that DFT/IDFT are in terms of +/- frequency >>> rather than frequency/phase} >> I'd actually thought this might be an answer, but wasn't sure. >> It seemed too obvious. >> >>> That would seem to meet your *SPECIFICATION* . >>> *_HOWEVER_* I've a gut feeling it may not meet your need. >>> How would you phrase your need if you were operating purely in the >>> analog domain? >> I am thinking about trying to investigate adding various kinds of >> well-known distortions to PCM streams. This partly as part of a >> recording hobby, partly to learn about them. > > are you trying to introduce a specified amount of specific harmonics > to a pure sine wave? No, for any random PCM stream. > if that is how you want to wrap the problem > statement, then i would suggest you look into polynomials, and > specifically Tchebyshev polynomials. but any general Nth-order > polynomial will generate harmonics up to the Nth harmonic. > > r b-j -- Les Cargill
From: Les Cargill on 8 Mar 2010 16:35 Jerry Avins wrote: > Jerry Avins wrote: > > ... > >> I don't know of a comprehensive treatment. ... > > People who try to build semiconductor amplifiers that sound like tube > amplifiers dig deeply into controlled distortion. That avenue might > provide some leads. > > Jerry I actually started thinking about this after reading much of the Pass DIY website. -- Les Cargill
From: Les Cargill on 8 Mar 2010 17:19 Jerry Avins wrote: > Les Cargill wrote: >> robert bristow-johnson wrote: > > ... > >>> are you trying to introduce a specified amount of specific harmonics >>> to a pure sine wave? >> >> No, for any random PCM stream. > > As I see it, the answer is a non-sequitur. > > ... > > Jerry How about "for any *arbitrary* PCM stream?" -- Les Cargill
From: dvsarwate on 8 Mar 2010 18:08
On Mar 8, 4:19 pm, Les Cargill <lcargil...(a)comcast.net> wrote: > Jerry Avins wrote: > > Les Cargill wrote: > >> robert bristow-johnson wrote: > > > ... > > >>> are you trying to introduce a specified amount of specific harmonics > >>> to a pure sine wave? > > >> No, for any random PCM stream. > > > As I see it, the answer is a non-sequitur. > > > ... > > > Jerry > > How about "for any *arbitrary* PCM stream?" > > -- > Les Cargill Perhaps the OP should be more clear as to what exactly he wants. For a pure sinusoid, say s(t) = 3cos(wt), whether as an analog signal or as a PCM stream, we can add in second harmonic distortion by adding (say) 0.1s^2(t) to s(t) and subtracting off the DC term thus introduced. But using a cubic adds in a third harmonic and also changes the amplitude of the fundamental. Is this OK? Or does harmonic distortion in this instance mean 0.1cos(3wt) gets added to s(t) with no change in the fundamental? Turning to more arbitrary signals, if s(t) = 3 sin(w1t) + 4 sin(w2t), then adding in (say) 0.1s^2(t) to s(t) adds in second harmonics of w1 and w2 but also intermodulation products at frequencies w1+w2 and w1-w2. Is this OK? Or are looking to change s(t) = 3 sin(w1t) + 4 sin(w2t) by adding in (say) 0.1sin(2w1t) + 0.2sin(2w2t)? Pure harmonic distortion and *no* intermodulation distortion? And what exactly does the OP mean by harmonic distortion of a random or arbitrary data stream which is not necessarily periodic at all. Absent a fundamental, what is *harmonic* distortion? --Dilip Sarwate |