FA-91733 / Digital signal filters / Member archive

Goertzel uses cos(w) as the resonator coefficient · case 03

The resonator is tuned to the wrong frequency and DC input does not accumulate linearly.

Member previewVariant 3 · 3 implementations · 7 checks per implementation

Case contract

Input [N, k, samples]; samples must have length N ("length-mismatch"). Goertzel recursion s = x + c s1 - s2 with c = 2 cos(2 pi k / N) from zero state; power = s1^2 + s2^2 - c s1 s2, rounded to 6 decimals (equals |X[k]|^2 of the DFT).

Why this case matters

Goertzel filters detect single tones cheaply (DTMF, pilot tones); recursion or coefficient slips misreport bin energy.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
regression: random goertzel 3	`11.945195`	`7.416002`	Failed

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