FA-91527 / Digital signal filters / Member archive

Frequency response evaluates z^-k as e^{+jwk} · case 02

Magnitudes are right but every phase has the opposite sign; a pure delay shows phase lead.

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: pure delay phase	`[[0.0, 45.0], [0.0, 90.0]]`	`[[0.0, -45.0], [0.0, -90.0]]`	Failed

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