FA-91820 / Digital signal filters / Member archive

Notch design places the zeros at pi - w0 · case 05

The notch appears at fs/2 - f0.

Member previewVariant 5 · 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=3 fs=8 r=0	`{"a": [1.0, 0.0, 0.0], "b": [1.707106781, -2.414213562, 1.707106781]}`	`{"a": [1.0, 0.0, 0.0], "b": [0.292893219, 0.414213562, 0.292893219]}`	Failed

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