Interesting Paper available on Moog VCF

[Eli Brandt]

Don Tillman wrote:
>    Interesting.  My gut feeling is that if the waveshaping function is
>    "smooth" in some sense, it should produce a band-limited output.  
> 
> Only for a few special case curves.  Square-law f'rinstance.

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.

If we're stuck with infinite harmonics coming out of our waveshaping,
the conceptually simplest solution would be to supersample, waveshape,
lowpass, and subsample.  The crud probably falls off at least
inverse-linearly with frequency, so moderate oversampling shuold
substantially reduce the amount of energy that gets sprayed into your
spectrum: n-times gives a reduction of 2n-1.

   |
   |   |                        hits 22kHz here --------v
   |   |   |   |   |   |   
   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |
   +----------+--------------------+--------------------+
             22k                 n*22k            (2n-1)*22k

This chain of operations might simplify, but probably not.  I've
considered just doing all digital work at a multiple of audio rate,
and lowpassing whenever spurious harmonics are generated.  This costs
you a constant factor everywhere, but avoids the expense of resampling
up and down all over the place.

-- 
. Eli Brandt                                            usual disclaimers .
. eli+ at cs.cmu.edu                                      PGP key on request .
. "Certain deliberate disturbances of the beat are extremely beautiful."  .
.       -- C.P.E. Bach                                                    .