FA-91777 / Digital signal filters / Member archive

Impulse truncation treats any negative sample as quiet · case 02

An alternating response is cut at its first large negative sample.

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: gap inside numerator with pole	`["1", "-1/4", "1/16", "127/64", "-127/256"]`	`["1", "-1/4", "1/16", "127/64", "-127/256", "127/1024"]`	Failed

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