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FA-91551 / Digital signal filters / Open access

Polyphase decimator reads negative indices from the end of the signal · case 01

Early outputs pick up samples from the tail of the buffer.

Verified by executionVariant 1 · 7 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The bounds test only checks idx < L, so negative indices wrap around.

VERIFIED REPAIR

Require 0 <= idx < L.

Unsuccessful approach: The attempted repair uses 0 < idx, dropping x[0].

Case contract

Input [h, D, samples] (integers). Output y[m] = sum_k h[k] x[mD - k] for m = 0 .. ceil(len/D) - 1 with x = 0 outside the signal, computed through the polyphase split E_p[j] = h[jD + p].

Why this case matters

Polyphase decimators avoid computing discarded outputs; commutator and phase-split slips alias the output.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    h, D, xs = x
    L = len(xs)
    M = (L + D - 1) // D
    phases = [h[p::D] for p in range(D)]
    out = []
    for m in range(M):
        acc = 0
        for p in range(D):
            for j, c in enumerate(phases[p]):
                idx = (m - j) * D - p
                if idx < L:
                    acc += c * xs[idx]
        out.append(acc)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: length divisible', [[1, 1], 2, [1, 2, 3, 4]], [1, 5]], ['regression: long filter D=3', [[1, 2, 3, 4, 5], 3, [1, 0, 0, 2, 0, 0, 3]], [1, 6, 11]], ['repair check: impulse through D=2', [[1, 2, 3], 2, [1, 0, 0, 0, 0]], [1, 3, 0]], ['control: random polyphase 30', [[-1], 4, [0, -3, 0, -4, 4, 5]], [0, -4]], ['control: random polyphase 48', [[4], 2, [0, 5, 4, 2, 1, -1, 0, -3]], [0, 16, 4, 0]], ['regression: random polyphase 0', [[2, -1], 2, [3, -3, 4, -2, -3, 5, 1]], [6, 11, -4, -3]], ['regression: random polyphase 1', [[-2, 4, -1, -1, 1, -3], 4, [3, 0, 1, 0, -1, -2]], [-6, 4]]], [['regression: random polyphase 1', [[-2, 4, -1, -1, 1, -3], 4, [3, 0, 1, 0, -1, -2]], [-6, 4]], ['regression: random polyphase 2', [[4, 2, 3, -2, 4], 4, [-2, -4, 3, 0, -1, -2, 3, -1]], [-8, 5]], ['repair check: first sample matters', [[1], 3, [7, 1, 1, 1]], [7, 1]], ['control: random polyphase 30', [[-1], 4, [0, -3, 0, -4, 4, 5]], [0, -4]], ['control: random polyphase 48', [[4], 2, [0, 5, 4, 2, 1, -1, 0, -3]], [0, 16, 4, 0]], ['regression: random polyphase 0', [[2, -1], 2, [3, -3, 4, -2, -3, 5, 1]], [6, 11, -4, -3]], ['regression: random polyphase 4', [[0, -1, 1, -1, 4], 3, [3, 2, 5, 3, -1, 0, -3, 2, -1, -2]], [0, -6, 16, 6]]], [['regression: random polyphase 5', [[3, 1, -1, 0, -1], 2, [-3, 5, 4, 1]], [-9, 20]], ['regression: random polyphase 6', [[1, -2, 3, 2, -1], 4, [4, 3, 5, -3, -4, -2]], [4, 19]], ['regression: random polyphase 0', [[2, -1], 2, [3, -3, 4, -2, -3, 5, 1]], [6, 11, -4, -3]], ['control: random polyphase 30', [[-1], 4, [0, -3, 0, -4, 4, 5]], [0, -4]], ['control: random polyphase 48', [[4], 2, [0, 5, 4, 2, 1, -1, 0, -3]], [0, 16, 4, 0]], ['regression: random polyphase 1', [[-2, 4, -1, -1, 1, -3], 4, [3, 0, 1, 0, -1, -2]], [-6, 4]], ['regression: random polyphase 2', [[4, 2, 3, -2, 4], 4, [-2, -4, 3, 0, -1, -2, 3, -1]], [-8, 5]]], [['regression: random polyphase 9', [[1, -2, 2, 3, 1, 0], 3, [5, 2, 1, -3, 4, 0, 0, 1]], [5, 14, 0]], ['regression: random polyphase 10', [[3, -1, 1, 0, -2, 2], 4, [3, -3, 0, -3, 2, 1]], [9, 3]], ['regression: random polyphase 2', [[4, 2, 3, -2, 4], 4, [-2, -4, 3, 0, -1, -2, 3, -1]], [-8, 5]], ['control: random polyphase 30', [[-1], 4, [0, -3, 0, -4, 4, 5]], [0, -4]], ['control: random polyphase 48', [[4], 2, [0, 5, 4, 2, 1, -1, 0, -3]], [0, 16, 4, 0]], ['regression: random polyphase 4', [[0, -1, 1, -1, 4], 3, [3, 2, 5, 3, -1, 0, -3, 2, -1, -2]], [0, -6, 16, 6]], ['regression: random polyphase 5', [[3, 1, -1, 0, -1], 2, [-3, 5, 4, 1]], [-9, 20]]], [['regression: random polyphase 12', [[-2, 3, 1, -3, 1, 2, 3], 3, [2, 5, 1, 5, -2, -2]], [-4, -8]], ['regression: random polyphase 13', [[1, 4], 2, [-4, 3, -1, 4]], [-4, 11]], ['regression: random polyphase 4', [[0, -1, 1, -1, 4], 3, [3, 2, 5, 3, -1, 0, -3, 2, -1, -2]], [0, -6, 16, 6]], ['control: random polyphase 30', [[-1], 4, [0, -3, 0, -4, 4, 5]], [0, -4]], ['control: random polyphase 48', [[4], 2, [0, 5, 4, 2, 1, -1, 0, -3]], [0, 16, 4, 0]], ['regression: random polyphase 5', [[3, 1, -1, 0, -1], 2, [-3, 5, 4, 1]], [-9, 20]], ['regression: random polyphase 6', [[1, -2, 3, 2, -1], 4, [4, 3, 5, -3, -4, -2]], [4, 19]]]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
regression: length divisible[5, 5][1, 5]Failed
regression: long filter D=3[17, 21, 11][1, 6, 11]Failed
repair check: impulse through D=2[1, 3, 0][1, 3, 0]Passed
control: random polyphase 30[0, -4][0, -4]Passed
control: random polyphase 48[0, 16, 4, 0][0, 16, 4, 0]Passed
regression: random polyphase 0[5, 11, -4, -3][6, 11, -4, -3]Failed
regression: random polyphase 1[-12, 10][-6, 4]Failed

SHA-256 / f04ec33bad8f869e0515477dbe8f8b20791e19351591cfc9a0ecddf767d83a15

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    h, D, xs = x
    L = len(xs)
    M = (L + D - 1) // D
    phases = [h[p::D] for p in range(D)]
    out = []
    for m in range(M):
        acc = 0
        for p in range(D):
            for j, c in enumerate(phases[p]):
                idx = (m - j) * D - p
                if 0 < idx < L:
                    acc += c * xs[idx]
        out.append(acc)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: length divisible', [[1, 1], 2, [1, 2, 3, 4]], [1, 5]], ['regression: long filter D=3', [[1, 2, 3, 4, 5], 3, [1, 0, 0, 2, 0, 0, 3]], [1, 6, 11]], ['repair check: impulse through D=2', [[1, 2, 3], 2, [1, 0, 0, 0, 0]], [1, 3, 0]], ['control: random polyphase 30', [[-1], 4, [0, -3, 0, -4, 4, 5]], [0, -4]], ['control: random polyphase 48', [[4], 2, [0, 5, 4, 2, 1, -1, 0, -3]], [0, 16, 4, 0]], ['regression: random polyphase 0', [[2, -1], 2, [3, -3, 4, -2, -3, 5, 1]], [6, 11, -4, -3]], ['regression: random polyphase 1', [[-2, 4, -1, -1, 1, -3], 4, [3, 0, 1, 0, -1, -2]], [-6, 4]]], [['regression: random polyphase 1', [[-2, 4, -1, -1, 1, -3], 4, [3, 0, 1, 0, -1, -2]], [-6, 4]], ['regression: random polyphase 2', [[4, 2, 3, -2, 4], 4, [-2, -4, 3, 0, -1, -2, 3, -1]], [-8, 5]], ['repair check: first sample matters', [[1], 3, [7, 1, 1, 1]], [7, 1]], ['control: random polyphase 30', [[-1], 4, [0, -3, 0, -4, 4, 5]], [0, -4]], ['control: random polyphase 48', [[4], 2, [0, 5, 4, 2, 1, -1, 0, -3]], [0, 16, 4, 0]], ['regression: random polyphase 0', [[2, -1], 2, [3, -3, 4, -2, -3, 5, 1]], [6, 11, -4, -3]], ['regression: random polyphase 4', [[0, -1, 1, -1, 4], 3, [3, 2, 5, 3, -1, 0, -3, 2, -1, -2]], [0, -6, 16, 6]]], [['regression: random polyphase 5', [[3, 1, -1, 0, -1], 2, [-3, 5, 4, 1]], [-9, 20]], ['regression: random polyphase 6', [[1, -2, 3, 2, -1], 4, [4, 3, 5, -3, -4, -2]], [4, 19]], ['regression: random polyphase 0', [[2, -1], 2, [3, -3, 4, -2, -3, 5, 1]], [6, 11, -4, -3]], ['control: random polyphase 30', [[-1], 4, [0, -3, 0, -4, 4, 5]], [0, -4]], ['control: random polyphase 48', [[4], 2, [0, 5, 4, 2, 1, -1, 0, -3]], [0, 16, 4, 0]], ['regression: random polyphase 1', [[-2, 4, -1, -1, 1, -3], 4, [3, 0, 1, 0, -1, -2]], [-6, 4]], ['regression: random polyphase 2', [[4, 2, 3, -2, 4], 4, [-2, -4, 3, 0, -1, -2, 3, -1]], [-8, 5]]], [['regression: random polyphase 9', [[1, -2, 2, 3, 1, 0], 3, [5, 2, 1, -3, 4, 0, 0, 1]], [5, 14, 0]], ['regression: random polyphase 10', [[3, -1, 1, 0, -2, 2], 4, [3, -3, 0, -3, 2, 1]], [9, 3]], ['regression: random polyphase 2', [[4, 2, 3, -2, 4], 4, [-2, -4, 3, 0, -1, -2, 3, -1]], [-8, 5]], ['control: random polyphase 30', [[-1], 4, [0, -3, 0, -4, 4, 5]], [0, -4]], ['control: random polyphase 48', [[4], 2, [0, 5, 4, 2, 1, -1, 0, -3]], [0, 16, 4, 0]], ['regression: random polyphase 4', [[0, -1, 1, -1, 4], 3, [3, 2, 5, 3, -1, 0, -3, 2, -1, -2]], [0, -6, 16, 6]], ['regression: random polyphase 5', [[3, 1, -1, 0, -1], 2, [-3, 5, 4, 1]], [-9, 20]]], [['regression: random polyphase 12', [[-2, 3, 1, -3, 1, 2, 3], 3, [2, 5, 1, 5, -2, -2]], [-4, -8]], ['regression: random polyphase 13', [[1, 4], 2, [-4, 3, -1, 4]], [-4, 11]], ['regression: random polyphase 4', [[0, -1, 1, -1, 4], 3, [3, 2, 5, 3, -1, 0, -3, 2, -1, -2]], [0, -6, 16, 6]], ['control: random polyphase 30', [[-1], 4, [0, -3, 0, -4, 4, 5]], [0, -4]], ['control: random polyphase 48', [[4], 2, [0, 5, 4, 2, 1, -1, 0, -3]], [0, 16, 4, 0]], ['regression: random polyphase 5', [[3, 1, -1, 0, -1], 2, [-3, 5, 4, 1]], [-9, 20]], ['regression: random polyphase 6', [[1, -2, 3, 2, -1], 4, [4, 3, 5, -3, -4, -2]], [4, 19]]]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
regression: length divisible[0, 5][1, 5]Failed
regression: long filter D=3[0, 2, 11][1, 6, 11]Failed
repair check: impulse through D=2[0, 0, 0][1, 3, 0]Failed
control: random polyphase 30[0, -4][0, -4]Passed
control: random polyphase 48[0, 16, 4, 0][0, 16, 4, 0]Passed
regression: random polyphase 0[0, 11, -4, -3][6, 11, -4, -3]Failed
regression: random polyphase 1[0, 1][-6, 4]Failed

SHA-256 / 0061fb35459caee75ede7ffd41504bac17f91c29e0aad54622643229a48647ea

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(x):
    h, D, xs = x
    L = len(xs)
    M = (L + D - 1) // D
    phases = [h[p::D] for p in range(D)]
    out = []
    for m in range(M):
        acc = 0
        for p in range(D):
            for j, c in enumerate(phases[p]):
                idx = (m - j) * D - p
                if 0 <= idx < L:
                    acc += c * xs[idx]
        out.append(acc)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: length divisible', [[1, 1], 2, [1, 2, 3, 4]], [1, 5]], ['regression: long filter D=3', [[1, 2, 3, 4, 5], 3, [1, 0, 0, 2, 0, 0, 3]], [1, 6, 11]], ['repair check: impulse through D=2', [[1, 2, 3], 2, [1, 0, 0, 0, 0]], [1, 3, 0]], ['control: random polyphase 30', [[-1], 4, [0, -3, 0, -4, 4, 5]], [0, -4]], ['control: random polyphase 48', [[4], 2, [0, 5, 4, 2, 1, -1, 0, -3]], [0, 16, 4, 0]], ['regression: random polyphase 0', [[2, -1], 2, [3, -3, 4, -2, -3, 5, 1]], [6, 11, -4, -3]], ['regression: random polyphase 1', [[-2, 4, -1, -1, 1, -3], 4, [3, 0, 1, 0, -1, -2]], [-6, 4]]], [['regression: random polyphase 1', [[-2, 4, -1, -1, 1, -3], 4, [3, 0, 1, 0, -1, -2]], [-6, 4]], ['regression: random polyphase 2', [[4, 2, 3, -2, 4], 4, [-2, -4, 3, 0, -1, -2, 3, -1]], [-8, 5]], ['repair check: first sample matters', [[1], 3, [7, 1, 1, 1]], [7, 1]], ['control: random polyphase 30', [[-1], 4, [0, -3, 0, -4, 4, 5]], [0, -4]], ['control: random polyphase 48', [[4], 2, [0, 5, 4, 2, 1, -1, 0, -3]], [0, 16, 4, 0]], ['regression: random polyphase 0', [[2, -1], 2, [3, -3, 4, -2, -3, 5, 1]], [6, 11, -4, -3]], ['regression: random polyphase 4', [[0, -1, 1, -1, 4], 3, [3, 2, 5, 3, -1, 0, -3, 2, -1, -2]], [0, -6, 16, 6]]], [['regression: random polyphase 5', [[3, 1, -1, 0, -1], 2, [-3, 5, 4, 1]], [-9, 20]], ['regression: random polyphase 6', [[1, -2, 3, 2, -1], 4, [4, 3, 5, -3, -4, -2]], [4, 19]], ['regression: random polyphase 0', [[2, -1], 2, [3, -3, 4, -2, -3, 5, 1]], [6, 11, -4, -3]], ['control: random polyphase 30', [[-1], 4, [0, -3, 0, -4, 4, 5]], [0, -4]], ['control: random polyphase 48', [[4], 2, [0, 5, 4, 2, 1, -1, 0, -3]], [0, 16, 4, 0]], ['regression: random polyphase 1', [[-2, 4, -1, -1, 1, -3], 4, [3, 0, 1, 0, -1, -2]], [-6, 4]], ['regression: random polyphase 2', [[4, 2, 3, -2, 4], 4, [-2, -4, 3, 0, -1, -2, 3, -1]], [-8, 5]]], [['regression: random polyphase 9', [[1, -2, 2, 3, 1, 0], 3, [5, 2, 1, -3, 4, 0, 0, 1]], [5, 14, 0]], ['regression: random polyphase 10', [[3, -1, 1, 0, -2, 2], 4, [3, -3, 0, -3, 2, 1]], [9, 3]], ['regression: random polyphase 2', [[4, 2, 3, -2, 4], 4, [-2, -4, 3, 0, -1, -2, 3, -1]], [-8, 5]], ['control: random polyphase 30', [[-1], 4, [0, -3, 0, -4, 4, 5]], [0, -4]], ['control: random polyphase 48', [[4], 2, [0, 5, 4, 2, 1, -1, 0, -3]], [0, 16, 4, 0]], ['regression: random polyphase 4', [[0, -1, 1, -1, 4], 3, [3, 2, 5, 3, -1, 0, -3, 2, -1, -2]], [0, -6, 16, 6]], ['regression: random polyphase 5', [[3, 1, -1, 0, -1], 2, [-3, 5, 4, 1]], [-9, 20]]], [['regression: random polyphase 12', [[-2, 3, 1, -3, 1, 2, 3], 3, [2, 5, 1, 5, -2, -2]], [-4, -8]], ['regression: random polyphase 13', [[1, 4], 2, [-4, 3, -1, 4]], [-4, 11]], ['regression: random polyphase 4', [[0, -1, 1, -1, 4], 3, [3, 2, 5, 3, -1, 0, -3, 2, -1, -2]], [0, -6, 16, 6]], ['control: random polyphase 30', [[-1], 4, [0, -3, 0, -4, 4, 5]], [0, -4]], ['control: random polyphase 48', [[4], 2, [0, 5, 4, 2, 1, -1, 0, -3]], [0, 16, 4, 0]], ['regression: random polyphase 5', [[3, 1, -1, 0, -1], 2, [-3, 5, 4, 1]], [-9, 20]], ['regression: random polyphase 6', [[1, -2, 3, 2, -1], 4, [4, 3, 5, -3, -4, -2]], [4, 19]]]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
regression: length divisible[1, 5][1, 5]Passed
regression: long filter D=3[1, 6, 11][1, 6, 11]Passed
repair check: impulse through D=2[1, 3, 0][1, 3, 0]Passed
control: random polyphase 30[0, -4][0, -4]Passed
control: random polyphase 48[0, 16, 4, 0][0, 16, 4, 0]Passed
regression: random polyphase 0[6, 11, -4, -3][6, 11, -4, -3]Passed
regression: random polyphase 1[-6, 4][-6, 4]Passed

SHA-256 / a873a0d87497f60a27542a14c5c53d4df1d93b805095f5e2c5932df6793ccfc7

Verification & scope

A deterministic bounded teaching model with a stipulated toy contract; exact rational arithmetic or fixed-decimal rounding keeps outputs strict JSON. It is not a production DSP library and claims no standards conformance. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:51:36.955217+00:00.

Case digest / 740c79ee026ccb4296ccedd00b3f4dccbcfe91861c6b6827e5202424f77d658a