FA-91589 / Digital signal filters / Member archive

Stability test skips normalization by a0 · case 04

A denominator with a0 = 2 reports reflection coefficients twice too large and false instability.

Member previewVariant 4 · 3 implementations · 7 checks per implementation

Case contract

Input the denominator [a0, a1, ..., an] as rational strings. Normalize by a0 ("bad-a0" if missing or 0), drop trailing zero coefficients, then step down: k = last coefficient, unstable if |k| >= 1, else a_i <- (a_i - k a_{p-i}) / (1 - k^2) for i < p. Return {"stable": bool, "reflection": [k strings so far]}.

Why this case matters

Checking IIR denominators for stability before deployment prevents runaway filters; step-down slips accept unstable designs.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
regression: random denominator 24	`{"reflection": ["1/2"], "stable": true}`	`{"reflection": ["1/4"], "stable": true}`	Failed

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