FA-91788 / Digital signal filters / Member archive

Impulse truncation normalizes the denominator before the numerator · case 03

With a0 = 2 the numerator is never scaled and the response is twice too large.

Member previewVariant 3 · 3 implementations · 7 checks per implementation

Case contract

Input [b, a, eps, maxlen, hold]; normalize by a0 ("bad-a0"), compute the impulse response exactly and stop after hold consecutive samples with |h| < eps, counted only once n >= len(b) - 1 (any non-quiet sample resets the count), or at maxlen. Return the kept samples as fraction strings.

Why this case matters

FIR approximations of IIR filters truncate the impulse response; wrong stop rules cut real energy or run forever.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
regression: random impulse 8	`["1/2", "17/8", "-15/32", "-15/128"]`	`["-1/2", "-17/8", "15/32", "15/128"]`	Failed

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