FA-91485 / Digital signal filters / Member archive

Q15 smoother divides with truncation toward zero · case 05

Negative updates round differently from positive ones, producing an asymmetric limit cycle.

Member previewVariant 5 · 3 implementations · 7 checks per implementation

Case contract

Input [alpha, samples]; alpha is Q15 in [0, 32768] ("bad-alpha" otherwise). Inputs are saturated to int16; y += ((x - y) * alpha + 2**14) >> 15 (round half up on the Q15 product via arithmetic shift), starting at y = 0. Return the integer outputs.

Why this case matters

Fixed-point exponential smoothers run on microcontrollers; rounding direction and saturation slips cause bias and limit cycles.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
regression: random smoother 12	`[-7930, -2700, 15034]`	`[-7931, -2700, 15034]`	Failed

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