FA-91584 / Digital signal filters / Member archive

Stability step-down divides by 1 - k · case 04

Reflection coefficients after the first step are mis-scaled and stability verdicts flip.

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 22	`{"reflection": ["3/8", "1/16"], "stable": true}`	`{"reflection": ["3/8", "1/22"], "stable": true}`	Failed

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