Interesting Paper available on Moog VCF

Tom May ftom at
Thu Sep 19 22:34:30 CEST 1996

Eli Brandt writes:

>Okay, maybe this "smooth" would be more constraining than I thought. :->
>My hope is that "smooth" might correspond to something like finite
>support over the set of Chebychev polynomials, but I don't have an
>intuitive handle on non-linear waveshaping -- let's see how the math
>comes out.

Any polynomial with a finite number of terms will produce a band
limited output when used as a transfer function.  But the bandwidth of
the output will be N times the bandwidth of the input, where N is the
degree of the polynomial.  That pretty much falls out of the sin^2(x)
= (1 - cos(2x))/2 type of identity when you keep applying it for each
degree of the polynomial.  (Or am I making an analog gut feeling

A year or so ago I experimented with digital distortion and if you
warp your signal too far with, say, some kind of transcendental
function you do get a lot of horrible noise.  At lower frequencies
and/or with less distortion it's not so noisy.  I didn't have time to
think about it at the time or I would have tried using low order
polynomials and oversampling.  Actually, out = sgn(in) gave pretty
good results :-)


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