FA-91805 / Digital signal filters / Member archive

Q15 FIR pushes new samples onto the wrong end of the delay line · case 05

The impulse response comes out reversed for asymmetric taps.

Member previewVariant 5 · 3 implementations · 7 checks per implementation

Case contract

Input [coeffs, samples] as Q15 integers. Each output accumulates the full-precision products c_k x[n-k] (zero history) in a wide accumulator, then rounds once (add 2**14, arithmetic shift 15) and saturates to int16. Return {"y": outputs, "saturations": number of clipped outputs}.

Why this case matters

DSP MAC units keep guard bits and round once; per-product rounding or missing overflow accounting degrades fixed-point FIRs.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
regression: random q15 fir 13	`{"saturations": 0, "y": [9895, 1673]}`	`{"saturations": 0, "y": [-2458, -2595]}`	Failed

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