FA-91789 / Digital signal filters / Member archive

Impulse truncation normalizes the denominator before the numerator · case 04

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

Member previewVariant 4 · 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 11	`["-1", "-1/4", "-5/16", "-9/64", "-29/256", "-65/1024"]`	`["-1/2", "-1/8", "-5/32", "-9/128", "-29/512"]`	Failed

MEMBER ARCHIVE

The complete case is available to members.

This record includes three runnable implementations, regression fixtures, execution results, and source hashes.

Member access is invitation-based. Sign in with your invited account to inspect the sources.