FA-91787 / Digital signal filters / Member archive

Impulse truncation normalizes the denominator before the numerator · case 02

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

Member previewVariant 2 · 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 3	`["-1", "-3/4", "11/16", "-11/64", "11/256", "-11/1024", "11/4096"]`	`["1", "3/4", "-11/16", "11/64", "-11/256", "11/1024", "-11/4096"]`	Failed

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