Interesting Paper available on Moog VCF
Tom May
ftom at netcom.com
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
mistake?)
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 :-)
Tom.
More information about the Synth-diy
mailing list