FA-91633 / Digital signal filters / Member archive

SOS cascade clamps only the final output · case 03

Intermediate stages exceed the limit, so later stages see values the hardware could never produce.

Member previewVariant 3 · 3 implementations · 7 checks per implementation

Case contract

Input [gain, sections, limit, samples]; each section [b0, b1, b2, a1, a2] is a direct-form-I biquad (a0 = 1) with its own state. The input is scaled by gain, each section output is clamped to [-limit, limit] and the clamped value is both stored as that section's output state and fed to the next section. Return exact fraction strings.

Why this case matters

Cascaded second-order sections with per-stage saturation model fixed-point IIR hardware; state sharing or gain staging slips change clipping.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
regression: random cascade 12	`["-3/2", "2", "39/32", "-2", "2", "-111/2048"]`	`["-3/2", "2", "27/32", "-2", "2", "0"]`	Failed

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