FA-91479 / Digital signal filters / Member archive

Q15 smoother truncates the product without a rounding offset · case 04

Negative steps settle one LSB short of the input; the filter has a persistent downward bias.

Member previewVariant 4 · 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 14	`[-9744, -19389, -4824, -15172, -3816, -981, -7994]`	`[-9743, -19389, -4823, -15171, -3815, -981, -7993]`	Failed

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