FA-91782 / Digital signal filters / Member archive

Impulse truncation stops inside the numerator span · case 02

A numerator with internal zeros such as [1, 0, 0, 1] is truncated before its last tap takes effect.

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 45	`["0"]`	`["0", "-1", "4/3", "-7/36", "-29/108", "179/1296"]`	Failed

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