Le 2012-02-02 à 12:50:00, Patrice Colet a écrit :
De: "Ed Kelly" morph_2016@yahoo.co.uk Here is my first attempt at making a resonant lowpass filter using cpole~ and czero~ objects.
using biquad~ gives very nice results for resonant filtering, ggee audio filters show how it sounds. It should be possible to use vanilla's audio math objects only for the biquad mathematical functions instead of an external.
[biquad~] is actually a shortcut for a certain set of special cases of having (up to) two [cpole~] and two [czero~] at once.
It's related to how quadratics like ax²+bx+c can't be factorised into e(x-f)(x-g) in real space because you need negative square roots to make it always factorisable, otherwise the squareroot fails when b²-4ac < 0, which is also the condition for resonance ; yet e(x-f)(x-g) in complex space also covers things that are impossible in real ax²+bx+c.
So a real ax²+bx+c is something between a pair of [rpole~] and a pair of [cpole~]. It's equivalent to a pair of [cpole~] in which you force two numbers to be the same, and two other numbers to be negatives of each other.
When you have a pair of [rpole~], it's like specifying f and g as real numbers, and thus being unable to construct any «irreducible» quadratics (b²<4ac). the numbers that are negatives of each other are the ± square roots : ± sqrt(4ac-b²)/2a.
(I hope I didn't make a mistake, and if I did, I'd like to know)
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