FA-91705 / Digital signal filters / Member archive

Bilinear mapping uses K = fs · case 05

The digital cutoff lands at about half the intended frequency.

Member previewVariant 5 · 3 implementations · 7 checks per implementation

Case contract

Input [kind, wc, fs] with rational analog cutoff wc (rad/s) and sample rate fs. Map H(s) = wc/(s+wc) (lowpass) or s/(s+wc) (highpass) with s = K (1 - z^-1)/(1 + z^-1), K = 2 fs, no prewarping. Return {"b": [b0, b1], "a": [1, a1]} as fraction strings normalized so a0 = 1, or "bad-spec".

Why this case matters

The bilinear transform is the standard analog-to-digital mapping; K or sign slips move the cutoff or flip the filter type.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
regression: lowpass wc=3 fs=1/2	`{"a": ["1", "5/7"], "b": ["6/7", "6/7"]}`	`{"a": ["1", "1/2"], "b": ["3/4", "3/4"]}`	Failed

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