Is it possible to generate harmonic distortion analytically?
in [DSP]
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From: Les Cargill on 10 Mar 2010 00:51 robert bristow-johnson wrote: > On Mar 9, 11:30 pm, Jerry Avins <j...(a)ieee.org> wrote: >> Les Cargill wrote: >>> Mark wrote: >>>> On Mar 8, 8:20 pm, Les Cargill <lcargil...(a)comcast.net> wrote: >>>>> Jerry Avins wrote: >>>>>> Les Cargill 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?" >>>>>> That doesn't fix it. I wasn't picking nits. The question was, given any >>>>>> arbitrary waveform, what harmonics do you want to add to it. >>>>> The usual suspects - second, third, fifth. >>>>>> An answer >>>>>> pins down a process that applies to any waveform, whether it be random >>>>>> or have a familiar name. >>>>> Ah! Thanks! >>>>>> Jerry >>>>> -- >>>>> Les Cargill- Hide quoted text - >>>>> - Show quoted text - >>>> I may be missing something in the discussion but I think the simple >>>> answer to your question is: >>>> the second harmonic component is created by the A*x^2 term and the the >>>> third harmonic component is created by the B*x^3 term etc of the >>>> transfer function. The (complex) magnitude of the coefficents A and >>>> B etc determine the magnitude (and phase) of the varous harmonics. >>>> Is that what you were asking? >>>> Mark >>> I believe it is. >> But be aware that the x^3 term can affect the amplitude of the >> fundamental/ I need to think more about the phase. > > i don't think that memoryless mapping functions can do much about > phase except maybe flip the polarity. > > now, for Les and Mark. yes, in general, an Nth-order polynomial will > create, out of a single sinusoid, new frequencies that are harmonic up > to the Nth harmonic. But the generation of harmonics is level > dependent (as it is for any non-linear distortion). > > now, if you *know* or can assume the level of your sinusoid, you can > create an Nth-order polynomial that will create a specified level of > each harmonic up to the Nth harmonic. you define your Nth-order > polynomial as a sum of Tchebyshev polynomials up to the Nth-order > Tchebyshev. if a normalized sinusoid goes into a 5th-order > Tchebyshev, what comes out is only the 5th harmonic and no others. > now, does that help you, Les, regarding the "generate harmonic > distortion analytically"? > It very much sounds like it does. Yes, the Tchebyshev polynomials look like what I'm looking for. Sorry - I should have said as much when you brought them up upthread. I am not *sure*, of course - but just going over them a bit, I think I see what's up. Heh. Look here: http://www.ecs.fullerton.edu/~mathews/n2003/chebyshevpoly/ChebyshevPolyProof.pdf That's exactly what I was thinking of, right there, I bet. > otherwise, i think you need to be more specific about the nature of > your input signal. Just garden varieties of audio. Nothing fancy. Music, basically. > > r b-j -- Les Cargill
From: Frnak McKenney on 10 Mar 2010 08:44 On Tue, 09 Mar 2010 23:30:03 -0500, Jerry Avins <jya(a)ieee.org> wrote: [...] > But be aware that the x^3 term can affect the amplitude of the > fundamental/ I need to think more about the phase. > > Jerry Isn't that the fundamental purpose of DSP? Taking the data you are given and putting a good phase on it? <grin> Frank McKenney -- If teachers now lack the knowledge they need to teach reading and other subjects well, it is not because they are innately incompetent but because they have been trained under faulty romantic ideas about the nature of reading and the worthlessness of "mere iformation". -- E.D. Hirsch, Jr./The Knowledge Deficit -- Frank McKenney, McKenney Associates Richmond, Virginia / (804) 320-4887 Munged E-mail: frank uscore mckenney ayut mined spring dawt cahm (y'all)
From: dvsarwate on 10 Mar 2010 10:11 On Mar 10, 7:44 am, Frnak McKenney <fr...(a)far.from.the.madding.crowd.com> wrote: > Isn't that the fundamental purpose of DSP? Taking the data you are > given and putting a good phase on it? Yes, but too many people are fazed by the tasks they have to carry out to accomplish the purpose....
From: Rune Allnor on 10 Mar 2010 10:23 On 10 Mar, 16:11, dvsarwate <dvsarw...(a)gmail.com> wrote: > On Mar 10, 7:44 am, Frnak McKenney > > <fr...(a)far.from.the.madding.crowd.com> wrote: > > Isn't that the fundamental purpose of DSP? Taking the data you are > > given and putting a good phase on it? > > Yes, but too many people are fazed by the tasks > they have to carry out to accomplish the purpose.... Yep - some people just can't face the problems... Rune
From: Vladimir Vassilevsky on 10 Mar 2010 10:26
robert bristow-johnson wrote: > otherwise, i think you need to be more specific about the nature of > your input signal. OP just wants to hear how the different levels of THD sound like. He couldn't put this straight because he is a lamer. BTW, what could be a procedure of creating a nonlinear function which produces the same gross amount of THD on a sine wave regardless of the amplitude? VLV |