FA-91360 / Digital signal filters / Member archive

Biquad adds the feedback terms · case 05

A filter specified with a1 = -1/2 (a decaying pole at +1/2) produces an alternating impulse response.

Member previewVariant 5 · 3 implementations · 7 checks per implementation

Case contract

Input [[b0, b1, b2, a0, a1, a2], samples]; coefficients are rational strings, normalized by a0 ("a0-zero" if a0 == 0). y[n] = b0 x[n] + b1 x[n-1] + b2 x[n-2] - a1 y[n-1] - a2 y[n-2] with zero initial state; return outputs as exact fraction strings.

Why this case matters

The biquad is the workhorse IIR section; sign, state or normalization slips produce unstable or wrong-gain filters.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
regression: random biquad 11	`["-3/2", "-5/4", "-37/24", "-623/144", "-2047/864"]`	`["-3/2", "-1/4", "65/24", "-409/144", "-1243/864"]`	Failed

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