At 2:47 PM -0800 12/13/04, Allan Hoeltje wrote:
>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.
i believe the trick is to form a partial differential from the signal and use the inverse Chebyshev to weight the differential equation.
The truth is I have no idea what you are trying to accomplish so I have really no idea what I'm telling you- are you sure you aren't trying to figure out the signal's frequency response?
The specific answer to your question is yes there is a way to derive an inverse Chebyshev filter however this may not be what you are actually asking for.
Good luck!
alex
>I have Googled for Inverse Chebychev (and Chebyshev) but have not found any
>formulas. Is there a way to derive an inverse Chebychev function?
>
>-Allan
>http://www.WholeCheese.com
>
>
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