FA-91840 / Digital signal filters / Member archive
Allpass swaps the input and output delay slots · case 05
The impulse response differs from the allpass kernel after the first sample.
Case contract
Input [a, samples]: y[n] = a x[n] + x[n-1] - a y[n-1] with zero state, "unstable" if |a| >= 1. Return exact fraction strings.
Why this case matters
Allpass sections build phase equalizers and fractional delays; any coefficient slip breaks the unit-magnitude property.
One recorded failure
Sample boundary fixtureThis sample comes from the broken implementation of a controlled reproducer.
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression: random allpass 9 | ["1/4", "-3/4", "3/4", "1/2", "-1/4", "1"] | ["1/4", "3/16", "-147/64", "1043/256", "749/1024", "-749/4096"] | Failed |
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