FA-91600 / Digital signal filters / Member archive

Coefficient quantizer rounds ties to even · case 05

0.125 at two fractional bits quantizes to code 0 instead of 1 (half away from zero).

Member previewVariant 5 · 3 implementations · 6 checks per implementation

Case contract

Input [coeffs, f, B, mode]: quantize each decimal coefficient to a B-bit two's-complement code with f fractional bits; "nearest" rounds half away from zero, "truncate" floors. Codes saturate to [-2^(B-1), 2^(B-1)-1]. Return {"codes", "saturated": count of clipped codes, "max_error": max |code/2^f - c| after saturation as a fraction string}.

Why this case matters

Coefficient quantization decides whether a fixed-point filter still meets spec; rounding and saturation slips shift poles.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
regression: tie cases nearest	`{"codes": [0, 2, 0], "max_error": "1/8", "saturated": 0}`	`{"codes": [1, 2, -1], "max_error": "1/8", "saturated": 0}`	Failed

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