[music-dsp] Blurps and Chirps when changing filter parameters

[Martin Eisenberg]

From: "Vadim Zavalishin" <vadim.zavalishin at native-instruments.de>

> >> (again I don't know where this method was described first).
> >
> > I believe that would be their ref. 4 (Borin et al. 2000)
which
> > introduced the K-method.

> I don't have access to that article, so unfortunately I cannot
> check that. I found another paper on a similar subject where
> one of the authors was the same in DAFX'04 proceedings
> (p.113), which is again on a subject of eliminating delay-free
> loops.

Ah yes, it seems the main difference is more structure in the
matrices in the newer paper. But it has occurred to me that you
perhaps meant the method of discretizing each integrator in an
analog structure by itself. Borin et al. 2000 doesn't allude to
that, and I'd be interested in any references you know of.

> Anyway, when I was referring to Serafini/Zamboni paper, the
> main thing I meant was that you can apply the bilinear
> transform directly to the differential equations, which
> eliminates the delay-free loops implicitly.

The BLT (trapezoidal rule) is an implicit integration scheme in
contrast to explicit methods like backward Euler, so it actually
preserves the analog model's instantaneous transmission and you
end up with the need for a numerical solver -- or in the scalar
linear case, the traditional structure-changing step of putting
the transfer function back on a single fraction line after
substituting for s.


Martin