[PD] more |vcf~| things

matthew jones mj at isvr.soton.ac.uk
Wed Mar 9 14:31:44 CET 2005

> 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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