FA-91770 / Digital signal filters / Member archive

DC blocker never updates its output history · case 05

The feedback path is dead and the blocker becomes a plain first difference.

Member previewVariant 5 · 3 implementations · 7 checks per implementation

Case contract

Input [R, samples]: y[n] = x[n] - x[n-1] + R y[n-1] with 0 <= R < 1 ("bad-pole"), warm-started so x[-1] = x[0] and y[-1] = 0 (no start-up step). Return exact fraction strings.

Why this case matters

DC blockers remove offsets before further processing; a cold start injects a large transient.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
regression: random dc blocker 13	`["0", "0", "1", "2", "-6", "7", "-8"]`	`["0", "0", "1", "11/4", "-63/16", "259/64", "-1271/256"]`	Failed

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