FA-91385 / Digital signal filters / Member archive

Transposed DF-II reads the output from the second state · case 05

The first output sample skips b1 contributions and the response is delayed by a sample.

Member previewVariant 5 · 3 implementations · 7 checks per implementation

Case contract

Input [[b0, b1, b2, a1, a2], samples, prime] (a0 = 1). Transposed direct form II: y = b0 x + s1; s1 = b1 x - a1 y + s2; s2 = b2 x - a2 y. If prime and samples exist, initialize s1, s2 to the steady state for a constant input equal to the first sample (y_ss = x0 (b0+b1+b2)/(1+a1+a2), "dc-pole" if the denominator is 0). Return exact fraction strings.

Why this case matters

Transposed DF-II is the default numerical form in filtering libraries, and steady-state priming avoids start-up transients.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
regression: random df2t 10	`["1/8", "-25/64", "281/512", "-793/4096", "-11495/32768"]`	`["1/8", "1/6", "-233/576", "2429/1728", "18953/41472"]`	Failed

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