FA-91442 / Digital signal filters / Member archive

CIC normalizes by R^N only · case 02

With M = 2 the output of a unit step settles at 2^N instead of 1.

Member previewVariant 2 · 3 implementations · 7 checks per implementation

Case contract

Input [N, R, M, samples]: N integrator stages at the input rate, keep the integrator output at indices R-1, 2R-1, ... (whole blocks only), then N comb stages y = v - v[k-M] at the low rate with zero initial state; divide by the gain (R M)^N and return exact fraction strings.

Why this case matters

CIC decimators front most digital down-converters; decimation phase, delay or gain slips distort the passband level.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
regression: random cic 4	`["-1", "2", "6", "4"]`	`["-1/2", "1", "3", "2"]`	Failed

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