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FA-91646 / Digital signal filters / Open access

Linear-phase delay ignores leading zero taps · case 01

[0, 0, 1, 2, 1] reports a delay of 1 sample instead of 3.

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

ROOT CAUSE

The delay is computed from the trimmed support only.

THE FAILURE

The delay is computed from the trimmed support only.

Unsuccessful approach: The attempted repair adds the number of trailing zeros instead.

Case contract

Input integer taps. Strip leading and trailing zeros ("degenerate" if all zero). The trimmed support of length N is type 1/2 if symmetric (odd/even N), type 3/4 if antisymmetric (odd/even N), otherwise not linear phase. Return {"type", "group_delay": leading zeros + (N-1)/2 as a fraction string} or both None.

Why this case matters

Linear-phase type determines which responses an FIR can realize (e.g. no highpass for type 2); misclassification picks the wrong design.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(x):
    h = list(x)
    lead = 0
    while lead < len(h) and h[lead] == 0:
        lead += 1
    if lead == len(h):
        return 'degenerate'
    end = len(h)
    while h[end - 1] == 0:
        end -= 1
    g = h[lead:end]
    N = len(g)
    sym = all(g[i] == g[N - 1 - i] for i in range(N))
    anti = all(g[i] == -g[N - 1 - i] for i in range(N))
    if sym:
        typ = 1 if N % 2 else 2
    elif anti:
        typ = 3 if N % 2 else 4
    else:
        return {'type': None, 'group_delay': None}
    return {'type': typ, 'group_delay': str(Fraction(N - 1, 2))}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: leading zeros symmetric', [0, 0, 1, 2, 1], {'type': 1, 'group_delay': '3'}], ['regression: padded type II', [0, 3, 3, 0, 0], {'type': 2, 'group_delay': '3/2'}], ['repair check: trailing zeros', [1, 2, 1, 0], {'type': 1, 'group_delay': '1'}], ['control: type III nonzero centre', [1, 2, -1], {'type': None, 'group_delay': None}], ['control: type III zero centre', [1, 0, -1], {'type': 3, 'group_delay': '1'}], ['control: type I', [1, 2, 1], {'type': 1, 'group_delay': '1'}], ['control: type II', [1, 1], {'type': 2, 'group_delay': '1/2'}]], [['regression: random linear phase 1', [0, 2, -2, 0, 0, 0], {'type': 4, 'group_delay': '3/2'}], ['regression: random linear phase 5', [0, 0, -3, -3, -2, -3, -3, 0], {'type': 1, 'group_delay': '4'}], ['regression: padded type II', [0, 3, 3, 0, 0], {'type': 2, 'group_delay': '3/2'}], ['control: type IV', [1, -1], {'type': 4, 'group_delay': '1/2'}], ['control: interior zero symmetric', [1, 0, 1], {'type': 1, 'group_delay': '1'}], ['control: all zero', [0, 0, 0], 'degenerate'], ['control: not linear phase', [1, 2, 3], {'type': None, 'group_delay': None}]], [['regression: random linear phase 10', [0, 0, 0, -1, 1, 0], {'type': 4, 'group_delay': '7/2'}], ['regression: random linear phase 11', [0, 0, 2, -2, 0], {'type': 4, 'group_delay': '5/2'}], ['repair check: random linear phase 0', [-1, -2, -1, 0, 1, 2, 1, 0], {'type': 3, 'group_delay': '3'}], ['control: type IV longer', [2, 1, -1, -2], {'type': 4, 'group_delay': '3/2'}], ['control: single tap', [5], {'type': 1, 'group_delay': '0'}], ['control: random linear phase 2', [0, 0, 2, 0, 2, 0, -2, 0, 0], {'type': None, 'group_delay': None}], ['control: random linear phase 4', [0, 1, -1, -1, 0], {'type': None, 'group_delay': None}]], [['regression: random linear phase 15', [0, 0, 1, -1, -1, 1, 0, 0], {'type': 2, 'group_delay': '7/2'}], ['regression: random linear phase 16', [0, -3, -1, 1, 3, 0, 0], {'type': 4, 'group_delay': '5/2'}], ['repair check: random linear phase 3', [1, 0, 1, 0], {'type': 1, 'group_delay': '1'}], ['control: random linear phase 6', [0, 3, 2, -3], {'type': None, 'group_delay': None}], ['control: random linear phase 7', [0, 0, 0, 0, 0], 'degenerate'], ['control: type III nonzero centre', [1, 2, -1], {'type': None, 'group_delay': None}], ['control: type III zero centre', [1, 0, -1], {'type': 3, 'group_delay': '1'}]], [['regression: random linear phase 18', [0, 0, 3, 3, 0, 0], {'type': 2, 'group_delay': '5/2'}], ['regression: random linear phase 20', [0, 2, -2, 2, 0, 0], {'type': 1, 'group_delay': '2'}], ['repair check: random linear phase 8', [2, -2, -2, 2, 2, -2, 0, 0], {'type': 4, 'group_delay': '5/2'}], ['control: type I', [1, 2, 1], {'type': 1, 'group_delay': '1'}], ['control: type II', [1, 1], {'type': 2, 'group_delay': '1/2'}], ['control: type IV', [1, -1], {'type': 4, 'group_delay': '1/2'}], ['control: interior zero symmetric', [1, 0, 1], {'type': 1, 'group_delay': '1'}]]]
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: leading zeros symmetric{'group_delay': '1', 'type': 1}{'group_delay': '3', 'type': 1}Failed
regression: padded type II{'group_delay': '1/2', 'type': 2}{'group_delay': '3/2', 'type': 2}Failed
repair check: trailing zeros{'group_delay': '1', 'type': 1}{'group_delay': '1', 'type': 1}Passed
control: type III nonzero centre{'group_delay': None, 'type': None}{'group_delay': None, 'type': None}Passed
control: type III zero centre{'group_delay': '1', 'type': 3}{'group_delay': '1', 'type': 3}Passed
control: type I{'group_delay': '1', 'type': 1}{'group_delay': '1', 'type': 1}Passed
control: type II{'group_delay': '1/2', 'type': 2}{'group_delay': '1/2', 'type': 2}Passed

SHA-256 / 1acd1a7f2623f11ff80ad0853921848d0e6cf0df63fb7afa8e0ef3a038717b5d

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(x):
    h = list(x)
    lead = 0
    while lead < len(h) and h[lead] == 0:
        lead += 1
    if lead == len(h):
        return 'degenerate'
    end = len(h)
    while h[end - 1] == 0:
        end -= 1
    g = h[lead:end]
    N = len(g)
    sym = all(g[i] == g[N - 1 - i] for i in range(N))
    anti = all(g[i] == -g[N - 1 - i] for i in range(N))
    if sym:
        typ = 1 if N % 2 else 2
    elif anti:
        typ = 3 if N % 2 else 4
    else:
        return {'type': None, 'group_delay': None}
    return {'type': typ, 'group_delay': str(len(h) - end + Fraction(N - 1, 2))}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: leading zeros symmetric', [0, 0, 1, 2, 1], {'type': 1, 'group_delay': '3'}], ['regression: padded type II', [0, 3, 3, 0, 0], {'type': 2, 'group_delay': '3/2'}], ['repair check: trailing zeros', [1, 2, 1, 0], {'type': 1, 'group_delay': '1'}], ['control: type III nonzero centre', [1, 2, -1], {'type': None, 'group_delay': None}], ['control: type III zero centre', [1, 0, -1], {'type': 3, 'group_delay': '1'}], ['control: type I', [1, 2, 1], {'type': 1, 'group_delay': '1'}], ['control: type II', [1, 1], {'type': 2, 'group_delay': '1/2'}]], [['regression: random linear phase 1', [0, 2, -2, 0, 0, 0], {'type': 4, 'group_delay': '3/2'}], ['regression: random linear phase 5', [0, 0, -3, -3, -2, -3, -3, 0], {'type': 1, 'group_delay': '4'}], ['regression: padded type II', [0, 3, 3, 0, 0], {'type': 2, 'group_delay': '3/2'}], ['control: type IV', [1, -1], {'type': 4, 'group_delay': '1/2'}], ['control: interior zero symmetric', [1, 0, 1], {'type': 1, 'group_delay': '1'}], ['control: all zero', [0, 0, 0], 'degenerate'], ['control: not linear phase', [1, 2, 3], {'type': None, 'group_delay': None}]], [['regression: random linear phase 10', [0, 0, 0, -1, 1, 0], {'type': 4, 'group_delay': '7/2'}], ['regression: random linear phase 11', [0, 0, 2, -2, 0], {'type': 4, 'group_delay': '5/2'}], ['repair check: random linear phase 0', [-1, -2, -1, 0, 1, 2, 1, 0], {'type': 3, 'group_delay': '3'}], ['control: type IV longer', [2, 1, -1, -2], {'type': 4, 'group_delay': '3/2'}], ['control: single tap', [5], {'type': 1, 'group_delay': '0'}], ['control: random linear phase 2', [0, 0, 2, 0, 2, 0, -2, 0, 0], {'type': None, 'group_delay': None}], ['control: random linear phase 4', [0, 1, -1, -1, 0], {'type': None, 'group_delay': None}]], [['regression: random linear phase 15', [0, 0, 1, -1, -1, 1, 0, 0], {'type': 2, 'group_delay': '7/2'}], ['regression: random linear phase 16', [0, -3, -1, 1, 3, 0, 0], {'type': 4, 'group_delay': '5/2'}], ['repair check: random linear phase 3', [1, 0, 1, 0], {'type': 1, 'group_delay': '1'}], ['control: random linear phase 6', [0, 3, 2, -3], {'type': None, 'group_delay': None}], ['control: random linear phase 7', [0, 0, 0, 0, 0], 'degenerate'], ['control: type III nonzero centre', [1, 2, -1], {'type': None, 'group_delay': None}], ['control: type III zero centre', [1, 0, -1], {'type': 3, 'group_delay': '1'}]], [['regression: random linear phase 18', [0, 0, 3, 3, 0, 0], {'type': 2, 'group_delay': '5/2'}], ['regression: random linear phase 20', [0, 2, -2, 2, 0, 0], {'type': 1, 'group_delay': '2'}], ['repair check: random linear phase 8', [2, -2, -2, 2, 2, -2, 0, 0], {'type': 4, 'group_delay': '5/2'}], ['control: type I', [1, 2, 1], {'type': 1, 'group_delay': '1'}], ['control: type II', [1, 1], {'type': 2, 'group_delay': '1/2'}], ['control: type IV', [1, -1], {'type': 4, 'group_delay': '1/2'}], ['control: interior zero symmetric', [1, 0, 1], {'type': 1, 'group_delay': '1'}]]]
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: leading zeros symmetric{'group_delay': '1', 'type': 1}{'group_delay': '3', 'type': 1}Failed
regression: padded type II{'group_delay': '5/2', 'type': 2}{'group_delay': '3/2', 'type': 2}Failed
repair check: trailing zeros{'group_delay': '2', 'type': 1}{'group_delay': '1', 'type': 1}Failed
control: type III nonzero centre{'group_delay': None, 'type': None}{'group_delay': None, 'type': None}Passed
control: type III zero centre{'group_delay': '1', 'type': 3}{'group_delay': '1', 'type': 3}Passed
control: type I{'group_delay': '1', 'type': 1}{'group_delay': '1', 'type': 1}Passed
control: type II{'group_delay': '1/2', 'type': 2}{'group_delay': '1/2', 'type': 2}Passed

SHA-256 / 94564daf2697543dfd790afb4842e23e7a7e847f9da4ea1f3de8cb92229a4a90

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 7 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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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 2026-09-29T14:51:38.101502+00:00.

Case digest / 80ca2f3ae48c31f5dcc03f3491f8fcc46135855eb7afffa1521b4e8a851a4f8c