FA-91833 / Digital signal filters / Member archive
Allpass passes the input without the a coefficient · case 03
The section is not allpass; its DC gain differs from 1.
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 3 | ["1", "-3/5", "-16/25", "548/125", "1481/625", "11182/3125"] | ["3/5", "1/25", "-128/125", "1884/625", "8723/3125", "26956/15625"] | Failed |
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