FA-91517 / Digital signal filters / Member archive

Frequency response treats Nyquist-relative input as sample-rate-relative · case 02

f = 1/2 (half Nyquist) is evaluated at Nyquist.

Member previewVariant 2 · 3 implementations · 7 checks per implementation

Case contract

Input [b, a, freqs]; coefficients and frequencies are numbers or rational strings, frequencies are fractions of Nyquist. For w = pi f evaluate H = B(e^{jw})/A(e^{jw}) with z^-k = e^{-jwk}; return per frequency [20 log10 |H| rounded to 4, phase in degrees rounded to 3], "pole" if |A| < 1e-12, "zero" if |H| < 1e-9.

Why this case matters

Magnitude and phase plots are how filters are verified; unit or sign slips misreport cutoff and delay.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
regression: deep notch	`[[6.0206, 0.0], [6.0034, 3.6]]`	`["zero", [-24.0378, -88.2]]`	Failed

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