# [music-dsp] Inverse Chebychev polynomials?

alex alex at foinc.com
Mon Dec 13 18:55:53 EST 2004

```At 3:35 PM -0800 12/13/04, Joshua Scholar wrote:
>I have to work so I can't look this up right now but I'd say:
>
>1. If you look up Chebychev approximations in a "numerical recipies" book
>you'll find a method.
>
>2. There's a fast method - if you warp the input then you can use a Discrete
>Cosine Transform and mess with the signs of the results a little bit to get
>polynomials in one step.

"Analog and Digital Filter Design using C" is a great book with exactly this warping method (otherwise known as the bilinear transform) by Les These.   You can find it at the library I believe.  It also contains the Inverse Chebyshev approximations and C code.

alex

>----- Original Message -----
>From: "Allan Hoeltje" <allan at wholecheese.com>
>To: "dsp list" <music-dsp at shoko.calarts.edu>
>Sent: Monday, December 13, 2004 2:30 PM
>Subject: [music-dsp] Inverse Chebychev polynomials?
>
>
>>
>> Sorry if this sounds like a dumb question for this list but I am still new
>> at dsp.  I want to do wave shaping signal distortion using Chebychev
>> polynomials.
>>
>> I am able to construc a wave shaping curve easy enough from the set of
>> polynomials defined by:
>>
>> Let C[0] represent the 0th Chebychev polynomial, C[1] the 1st, and C[n]
>the
>> nth, and so on.  C[0] = 1;  C[1] = x; and C[n] = 2xC[n-1] - C[n-2];  for x
>> in {-1...+1}
>>
>> What I still need to do is go the other way: derive the polynomial for a
>> given wave shape.
>>
>any
>> formulas.  Is there a way to derive an inverse Chebychev function?
>>
>> -Allan
>> http://www.WholeCheese.com
>>
>>
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```