FA-91758 / Digital signal filters / Member archive

DC blocker starts from a zero previous input · case 03

A constant input produces a decaying spike equal to the offset at start-up.

Member previewVariant 3 · 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 4	`["1", "7/4", "85/16", "-129/64", "-899/256"]`	`["0", "1", "19/4", "-39/16", "-245/64"]`	Failed

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