FA-91518 / Digital signal filters / Member archive

Frequency response treats Nyquist-relative input as sample-rate-relative · case 03

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

Member previewVariant 3 · 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: random response 1	`[[6.0206, 0.0], [5.563, -161.565], [-4.9961, -132.774]]`	`[[5.563, 161.565], [7.5974, 60.22], [-12.1798, -110.508]]`	Failed

MEMBER ARCHIVE

The complete case is available to members.

This record includes three runnable implementations, regression fixtures, execution results, and source hashes.

Member access is invitation-based. Sign in with your invited account to inspect the sources.