FA-91823 / Digital signal filters / Member archive

Notch design inverts the DC gain correction · case 03

The passband gain is squared away from unity instead of corrected.

Member previewVariant 3 · 3 implementations · 7 checks per implementation

Case contract

Input [f0, fs, r]: second-order notch with zeros on the unit circle at +-w0 (w0 = 2 pi f0 / fs) and poles at radius r: b = [1, -2 cos w0, 1], a = [1, -2 r cos w0, r^2]; b is scaled for unity DC gain (sum(a)/sum(b)). Coefficients rounded to 9 decimals; "bad-frequency" unless 0 < f0 < fs/2, "bad-radius" unless 0 <= r < 1.

Why this case matters

Notch filters remove mains hum and interference tones; angle or radius slips miss the tone or widen the notch.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
regression: f0=60 fs=480 r=1/2	`{"a": [1.0, -0.707106781, 0.25], "b": [1.079008574, -1.525948559, 1.079008574]}`	`{"a": [1.0, -0.707106781, 0.25], "b": [0.926776695, -1.310660172, 0.926776695]}`	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.