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PelleJuul / dsp-cookbook

The DSP Cookbook
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Biquad filter coefficient calculation derivations #1

Open PelleJuul opened 6 years ago

PelleJuul commented 6 years ago

I've have not been able to find a source for the derivations of the equations for calculating the filter coefficients for biquad filters. I'd like to include the derivations, so if anyone knows a nice source, please share it with me.

cerkut commented 6 years ago

General proofs are given by Robert Bristow-Johnson at [http://www.musicdsp.org/files/Audio-EQ-Cookbook.txt], and involve transforming analog filters to digital by bilinear transform. Park's proof for BP-Biquads (p226-227) is way simpler (but less general): he assumes a complex-conjugate pole pair, and parametrically solves for pole radius and angle.