FA-91515 / Digital signal filters / Member archive

Windowed sinc normalizes the peak tap to one · case 05

The DC gain is far above unity for long filters.

Member previewVariant 5 · 3 implementations · 7 checks per implementation

Case contract

Input [N, fc, window]; fc is the cutoff as a fraction of Nyquist in (0, 1], window hamming (0.54 - 0.46 cos(2 pi n/(N-1))), hann (0.5 - 0.5 cos(...)) or rect (N = 1 uses 1). Taps h[n] = fc sinc(fc (n - (N-1)/2)) w[n], normalized to unit DC gain and rounded to 8 decimals; "bad-spec" for invalid input (Hann needs N != 2).

Why this case matters

Windowed-sinc design is the default FIR recipe; centre or normalization slips yield non-linear-phase or wrong-gain filters.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
regression: N=4 fc=1/4 hann	`[0.0, 1.0, 1.0, 0.0]`	`[0.0, 0.5, 0.5, 0.0]`	Failed

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