Module dsp::biquad

#include <std/dsp/biquad.h> source

Biquad (2nd-order IIR section) + design tools

struct Biquad is a single Direct-Form-II-Transposed 2nd-order section:

y[n] = b0*x[n] + z1
z1'  = b1*x[n] - a1*y[n] + z2
z2'  = b2*x[n] - a2*y[n]

(a0 is always normalized to 1 — every coefficient below already has it divided out.) DF2T is the conventional choice for a single biquad: only two state variables, and better numerical behavior under coefficient quantization than Direct Form I. Cascade several for a higher-order filter (e.g. two biquads for a 4th-order response) with FilterChain (sample_filter.h): a chain of SampleFilters is itself one, so chains nest.

Biquad::lowpass/highpass/bandpass/notch/allpass/peaking/lowshelf/ highshelf compute coefficients using Robert Bristow-Johnson's "Audio EQ Cookbook" formulas — the standard, widely-implemented reference for these particular filter shapes. Biquad::bilinear is the more general tool underneath: given any analog (s-domain) 2nd-order prototype, it derives the matching digital biquad via the substitution s = 2fs(z-1)/(z+1) (the bilinear transform) — use it directly for an analog prototype the cookbook doesn't cover (e.g. a Butterworth/ Chebyshev/Bessel design), the same way the cookbook formulas were themselves derived from an analog prototype internally.

Structs

Biquad
Biquad32	Single precision (float coefficients and state), same contract as Biquad. The designers above compute in double; Biquad32::from rounds their result once (keeping its state).
FBiquad	Q8.24 fixed-point biquad: coefficients are designed in double precision via the designers above, then quantized once with FBiquad::from — the same design-time-float/runtime-fixed split as the rest of std/dsp.