[PD] more |vcf~| things
geiger at xdv.org
Thu Mar 10 10:42:40 CET 2005
AFAIK the vcf~ is a complex resonator filter, so it only has one pole.
The outputs of the vcf~ are real and imaginary part of the complex signal.
There is a nice description from Julius Smith on the CCRMA web:
On Wed, 9 Mar 2005, matthew jones wrote:
> > filters tend to
> > get an unlinear behaviour somehow, the closer the cutoff-freq gets to
> > the nyquist-frequency.
> > maybe someone else has a more 'academic' explanation for that behaviour.
> yeah, here goes:
> considering the filter in the z-plane, the poles (associated with the peak
> of the filter) occur in pairs: one is the conjugate of the other. This
> means that as you move the pole around from zero to pi, another pole mimics
> this, whose position is the same but reflected in the real axis. As you
> approach zero or pi, the peaks begin to merge into one, so there is a less
> rapid fall-off rate.
> Also the overall gain tends to increase for these regions, if fed white
> noise. This is simply to do with the superposition of the two responses
> (+ve and -ve freqs). The picture attached shows the response with a single
> pole at radius 0.6, first at pi/2 (black) and second at 4pi/5 (red).
> Than again, if I'm talking crap please correct me!
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