FA-91607 / Digital signal filters / Member archive

Coefficient quantizer allows the positive code 2^(B-1) · case 02

A coefficient of 1.0 in Q7 yields code 128, which does not fit in eight bits.

Member previewVariant 2 · 3 implementations · 7 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: random quantize 29	`{"codes": [8, -3, 8], "max_error": "3/50", "saturated": 0}`	`{"codes": [7, -3, 7], "max_error": "267/1000", "saturated": 2}`	Failed

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