# digital contents

Kimmo Koli kimmo at clara.hut.fi
Mon Sep 23 10:49:32 CEST 1996

```The difficult thing to make a nonlinear VCF in DSP in the resonance
feedback even with one nonlinear term in one integrator:

On 19 Sep 1996, Tom May wrote:

> Haible_Juergen#Tel2743 <HJ2743 at denbgm3xm.scnn1.msmgate.m30x.nbg.scn.de> writes:
>
> > Hmm, this is not AH, and you *can* build digital filters yourself,
> > nowadays, so I would have no problems with this.
> > Though I cannot contribute much to this DSP stuff myself,
> > I find it very interesting to see you talk about it. I'd appreciate
> > it if you go on with this nonlinearities/aliasing stuff.
>
> Ok, take the square law thing Don mentioned, say out = in + in^2.  For
> a sine input, the output will contain the original frequency, the
> second harmonic, and a DC component.  With more than one frequency in
> the input signal, the output will also contain all the f1+/-f2 cross
> terms (actually the DC and second harmonic is just a special case for
> f1=f2).  So like Don said, it is bandlimited because the highest
> output frequency will be no greater than twice the highest input
> frequency.  But, if that frequency exceeds half the sampling rate, it
> will be aliased and you will hear nastiness.
>

Resonance feedback brings back the doubled frequency and doubles it and
feeds it back and doubles it and ...

SO:
With feedback even the simplest nonlinearity produces an infinite
number of other frequencies!

AND:
Antialiasing this with an additional filter affects the pole locations
of the DSP VCF. These anti-alias filter poles should be at ten times higher
frequency at least in order not to move the VCF-poles. And this means quite
an increase in sampling frequency !

ALTERNATIVE:
Spice-transient analysis: numerical solutions of differential equations
of the nonlinear filter time step by time step. This means unknown number of
Newton iterations and numerical integration. This is not DSP, this is raw
floating-point calculation on a workstation. But with a well written
algorithm for this special case it may even work at slow realtime with a few
Alpha-chips in parallel...

It seems to me that REAL digital replacements of analog synths are not
here for a long time,
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Kimmo Koli      			     Email: kimmo at clara.hut.fi
Helsinki University of Technology          URL:   http://clara.hut.fi/~kimmo
Electronic Circuit Design Laboratory
Otakaari 5 A
FIN-02150 Espoo     			     Tel:  +358 0 451 2273
Finland      				     Fax:  +358 0 451 2269
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