FA-91830 / Digital signal filters / Member archive
Allpass adds the feedback term · case 05
The magnitude response is no longer flat; the section boosts low frequencies.
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 10 | ["-3/4", "-35/16", "269/64", "1165/256", "2445/1024"] | ["-3/4", "-29/16", "333/64", "563/256", "717/1024"] | Failed |
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