Cookbook formulae for audio equalizer biquad filter coefficients

Created: 2020-09-04T08:41:39+00:00

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Sometimes a0 is cancelled, and sometimes both a0 and b0 are cancelled.

Variables

Fs: the sampling frequency
f0: significant frequency
dBgain
Q, BW, and S: resonance, bandwidth or shelf slope

Includes math for high pass, low pass, band pass, notch, equalizer and shelf filters.

How the sausage is made

Based on an "analogue prototype," meaning ??? TODO. Think this means a transfer function designed for analogue hardware; ex. the ones you would need to use FFTs to actually implement.

Uses the "bilinear transform" and "pre-warping" to convert the analogue formula in to one solvable via the biquadratic filter equation.