FA-91461 / Digital signal filters / Open access

Median filter lets the window start wrap to the end · case 01

At the start of the signal the window slice is empty or picks samples from the end.

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

ROOT CAUSE

The start index is i - h without clipping; negative starts are interpreted from the end.

VERIFIED REPAIR

Clip the start at 0.

Unsuccessful approach: The attempted repair uses abs(i - h), which starts the window at a mirrored position.

Case contract

Input [K, samples]; K odd ("bad-kernel" otherwise). Output i is the median of samples[i-K//2 .. i+K//2] clipped to the valid range (shrinking windows at the edges); an even count uses the mean of the two middle values. Return exact fraction strings.

Why this case matters

Median filters remove impulse noise without blurring edges; window or tie handling slips shift features.

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):
    k, xs = x
    if k < 1 or k % 2 == 0:
        return 'bad-kernel'
    h = k // 2
    out = []
    for i in range(len(xs)):
        win = sorted(xs[i - h:i + h + 1])
        m = len(win)
        if m % 2:
            out.append(str(Fraction(win[m // 2])))
        else:
            out.append(str(Fraction(win[m // 2 - 1] + win[m // 2], 2)))
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: random median 26', [3, [-4, 5]], ['1/2', '1/2']], ['regression: random median 29', [5, [9, 8, 5]], ['8', '8', '8']], ['regression: random median 34', [3, [-1, 5]], ['2', '2']], ['control: even kernel', [2, [1, 2, 3]], 'bad-kernel'], ['control: even kernel four', [4, [1, 5, 2, 8]], 'bad-kernel'], ['control: random median 1', [1, [2, 3, 4, -2]], ['2', '3', '4', '-2']], ['control: random median 3', [1, [2, -3, 7, 8, -2, 3, 8, 1]], ['2', '-3', '7', '8', '-2', '3', '8', '1']]], [['regression: random median 40', [3, [0, 2]], ['1', '1']], ['regression: random median 44', [3, [9, 7]], ['8', '8']], ['regression: random median 34', [3, [-1, 5]], ['2', '2']], ['control: random median 7', [1, [7, 6, 6, -2, 6, 0, 8, -4]], ['7', '6', '6', '-2', '6', '0', '8', '-4']], ['control: random median 8', [1, [2, 8, -4, 9, 7, 7]], ['2', '8', '-4', '9', '7', '7']], ['control: random median 9', [1, [2, 5, 7, 9]], ['2', '5', '7', '9']], ['control: random median 10', [1, [9, 3, -5, 8]], ['9', '3', '-5', '8']]], [['regression: random median 29', [5, [9, 8, 5]], ['8', '8', '8']], ['regression: random median 34', [3, [-1, 5]], ['2', '2']], ['regression: random median 44', [3, [9, 7]], ['8', '8']], ['control: random median 14', [1, [2, 8, 6, 5, -4, -3, -1]], ['2', '8', '6', '5', '-4', '-3', '-1']], ['control: random median 15', [1, [8, 2]], ['8', '2']], ['control: random median 17', [1, [-5, -2, -4, 5, 9, 2, -4]], ['-5', '-2', '-4', '5', '9', '2', '-4']], ['control: random median 23', [1, [4, 1, -1, 3, -1]], ['4', '1', '-1', '3', '-1']]], [['regression: random median 44', [3, [9, 7]], ['8', '8']], ['regression: random median 26', [3, [-4, 5]], ['1/2', '1/2']], ['regression: random median 29', [5, [9, 8, 5]], ['8', '8', '8']], ['control: random median 25', [1, [-5, 6]], ['-5', '6']], ['control: random median 27', [1, [-2, 5, -4, 7, 1, -3]], ['-2', '5', '-4', '7', '1', '-3']], ['control: random median 28', [1, [1, -1, 2, 9, 2, 3, 6]], ['1', '-1', '2', '9', '2', '3', '6']], ['control: random median 35', [1, [-3, 0, 9]], ['-3', '0', '9']]], [['regression: random median 34', [3, [-1, 5]], ['2', '2']], ['regression: random median 40', [3, [0, 2]], ['1', '1']], ['regression: random median 44', [3, [9, 7]], ['8', '8']], ['control: random median 36', [1, [9, 8, 4]], ['9', '8', '4']], ['control: random median 37', [1, [-5, 8, 6, 4, -4, 5]], ['-5', '8', '6', '4', '-4', '5']], ['control: random median 39', [1, [3, 6, 4, 4, 1, -4, 9]], ['3', '6', '4', '4', '1', '-4', '9']], ['control: random median 41', [1, [2, 6]], ['2', '6']]]]
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 fixture	Actual	Expected	Outcome
regression: random median 26	`['5', '1/2']`	`['1/2', '1/2']`	Failed
regression: random median 29	`['13/2', '5', '8']`	`['8', '8', '8']`	Failed
regression: random median 34	`['5', '2']`	`['2', '2']`	Failed
control: even kernel	`bad-kernel`	`bad-kernel`	Passed
control: even kernel four	`bad-kernel`	`bad-kernel`	Passed
control: random median 1	`['2', '3', '4', '-2']`	`['2', '3', '4', '-2']`	Passed
control: random median 3	`['2', '-3', '7', '8', '-2', '3', '8', '1']`	`['2', '-3', '7', '8', '-2', '3', '8', '1']`	Passed

SHA-256 / f340ef53e4d2820171fc90c638110bbac80af8f8f9d976973f3a5633dbe76e2a

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):
    k, xs = x
    if k < 1 or k % 2 == 0:
        return 'bad-kernel'
    h = k // 2
    out = []
    for i in range(len(xs)):
        win = sorted(xs[abs(i - h):i + h + 1])
        m = len(win)
        if m % 2:
            out.append(str(Fraction(win[m // 2])))
        else:
            out.append(str(Fraction(win[m // 2 - 1] + win[m // 2], 2)))
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: random median 26', [3, [-4, 5]], ['1/2', '1/2']], ['regression: random median 29', [5, [9, 8, 5]], ['8', '8', '8']], ['regression: random median 34', [3, [-1, 5]], ['2', '2']], ['control: even kernel', [2, [1, 2, 3]], 'bad-kernel'], ['control: even kernel four', [4, [1, 5, 2, 8]], 'bad-kernel'], ['control: random median 1', [1, [2, 3, 4, -2]], ['2', '3', '4', '-2']], ['control: random median 3', [1, [2, -3, 7, 8, -2, 3, 8, 1]], ['2', '-3', '7', '8', '-2', '3', '8', '1']]], [['regression: random median 40', [3, [0, 2]], ['1', '1']], ['regression: random median 44', [3, [9, 7]], ['8', '8']], ['regression: random median 34', [3, [-1, 5]], ['2', '2']], ['control: random median 7', [1, [7, 6, 6, -2, 6, 0, 8, -4]], ['7', '6', '6', '-2', '6', '0', '8', '-4']], ['control: random median 8', [1, [2, 8, -4, 9, 7, 7]], ['2', '8', '-4', '9', '7', '7']], ['control: random median 9', [1, [2, 5, 7, 9]], ['2', '5', '7', '9']], ['control: random median 10', [1, [9, 3, -5, 8]], ['9', '3', '-5', '8']]], [['regression: random median 29', [5, [9, 8, 5]], ['8', '8', '8']], ['regression: random median 34', [3, [-1, 5]], ['2', '2']], ['regression: random median 44', [3, [9, 7]], ['8', '8']], ['control: random median 14', [1, [2, 8, 6, 5, -4, -3, -1]], ['2', '8', '6', '5', '-4', '-3', '-1']], ['control: random median 15', [1, [8, 2]], ['8', '2']], ['control: random median 17', [1, [-5, -2, -4, 5, 9, 2, -4]], ['-5', '-2', '-4', '5', '9', '2', '-4']], ['control: random median 23', [1, [4, 1, -1, 3, -1]], ['4', '1', '-1', '3', '-1']]], [['regression: random median 44', [3, [9, 7]], ['8', '8']], ['regression: random median 26', [3, [-4, 5]], ['1/2', '1/2']], ['regression: random median 29', [5, [9, 8, 5]], ['8', '8', '8']], ['control: random median 25', [1, [-5, 6]], ['-5', '6']], ['control: random median 27', [1, [-2, 5, -4, 7, 1, -3]], ['-2', '5', '-4', '7', '1', '-3']], ['control: random median 28', [1, [1, -1, 2, 9, 2, 3, 6]], ['1', '-1', '2', '9', '2', '3', '6']], ['control: random median 35', [1, [-3, 0, 9]], ['-3', '0', '9']]], [['regression: random median 34', [3, [-1, 5]], ['2', '2']], ['regression: random median 40', [3, [0, 2]], ['1', '1']], ['regression: random median 44', [3, [9, 7]], ['8', '8']], ['control: random median 36', [1, [9, 8, 4]], ['9', '8', '4']], ['control: random median 37', [1, [-5, 8, 6, 4, -4, 5]], ['-5', '8', '6', '4', '-4', '5']], ['control: random median 39', [1, [3, 6, 4, 4, 1, -4, 9]], ['3', '6', '4', '4', '1', '-4', '9']], ['control: random median 41', [1, [2, 6]], ['2', '6']]]]
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 fixture	Actual	Expected	Outcome
regression: random median 26	`['5', '1/2']`	`['1/2', '1/2']`	Failed
regression: random median 29	`['5', '13/2', '8']`	`['8', '8', '8']`	Failed
regression: random median 34	`['5', '2']`	`['2', '2']`	Failed
control: even kernel	`bad-kernel`	`bad-kernel`	Passed
control: even kernel four	`bad-kernel`	`bad-kernel`	Passed
control: random median 1	`['2', '3', '4', '-2']`	`['2', '3', '4', '-2']`	Passed
control: random median 3	`['2', '-3', '7', '8', '-2', '3', '8', '1']`	`['2', '-3', '7', '8', '-2', '3', '8', '1']`	Passed

SHA-256 / aa03df5a5557c0a43e15cec89a9a004e3e85191d40b5546a5ef8c4aca6a5bf64

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(x):
    k, xs = x
    if k < 1 or k % 2 == 0:
        return 'bad-kernel'
    h = k // 2
    out = []
    for i in range(len(xs)):
        win = sorted(xs[max(0, i - h):i + h + 1])
        m = len(win)
        if m % 2:
            out.append(str(Fraction(win[m // 2])))
        else:
            out.append(str(Fraction(win[m // 2 - 1] + win[m // 2], 2)))
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: random median 26', [3, [-4, 5]], ['1/2', '1/2']], ['regression: random median 29', [5, [9, 8, 5]], ['8', '8', '8']], ['regression: random median 34', [3, [-1, 5]], ['2', '2']], ['control: even kernel', [2, [1, 2, 3]], 'bad-kernel'], ['control: even kernel four', [4, [1, 5, 2, 8]], 'bad-kernel'], ['control: random median 1', [1, [2, 3, 4, -2]], ['2', '3', '4', '-2']], ['control: random median 3', [1, [2, -3, 7, 8, -2, 3, 8, 1]], ['2', '-3', '7', '8', '-2', '3', '8', '1']]], [['regression: random median 40', [3, [0, 2]], ['1', '1']], ['regression: random median 44', [3, [9, 7]], ['8', '8']], ['regression: random median 34', [3, [-1, 5]], ['2', '2']], ['control: random median 7', [1, [7, 6, 6, -2, 6, 0, 8, -4]], ['7', '6', '6', '-2', '6', '0', '8', '-4']], ['control: random median 8', [1, [2, 8, -4, 9, 7, 7]], ['2', '8', '-4', '9', '7', '7']], ['control: random median 9', [1, [2, 5, 7, 9]], ['2', '5', '7', '9']], ['control: random median 10', [1, [9, 3, -5, 8]], ['9', '3', '-5', '8']]], [['regression: random median 29', [5, [9, 8, 5]], ['8', '8', '8']], ['regression: random median 34', [3, [-1, 5]], ['2', '2']], ['regression: random median 44', [3, [9, 7]], ['8', '8']], ['control: random median 14', [1, [2, 8, 6, 5, -4, -3, -1]], ['2', '8', '6', '5', '-4', '-3', '-1']], ['control: random median 15', [1, [8, 2]], ['8', '2']], ['control: random median 17', [1, [-5, -2, -4, 5, 9, 2, -4]], ['-5', '-2', '-4', '5', '9', '2', '-4']], ['control: random median 23', [1, [4, 1, -1, 3, -1]], ['4', '1', '-1', '3', '-1']]], [['regression: random median 44', [3, [9, 7]], ['8', '8']], ['regression: random median 26', [3, [-4, 5]], ['1/2', '1/2']], ['regression: random median 29', [5, [9, 8, 5]], ['8', '8', '8']], ['control: random median 25', [1, [-5, 6]], ['-5', '6']], ['control: random median 27', [1, [-2, 5, -4, 7, 1, -3]], ['-2', '5', '-4', '7', '1', '-3']], ['control: random median 28', [1, [1, -1, 2, 9, 2, 3, 6]], ['1', '-1', '2', '9', '2', '3', '6']], ['control: random median 35', [1, [-3, 0, 9]], ['-3', '0', '9']]], [['regression: random median 34', [3, [-1, 5]], ['2', '2']], ['regression: random median 40', [3, [0, 2]], ['1', '1']], ['regression: random median 44', [3, [9, 7]], ['8', '8']], ['control: random median 36', [1, [9, 8, 4]], ['9', '8', '4']], ['control: random median 37', [1, [-5, 8, 6, 4, -4, 5]], ['-5', '8', '6', '4', '-4', '5']], ['control: random median 39', [1, [3, 6, 4, 4, 1, -4, 9]], ['3', '6', '4', '4', '1', '-4', '9']], ['control: random median 41', [1, [2, 6]], ['2', '6']]]]
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 fixture	Actual	Expected	Outcome
regression: random median 26	`['1/2', '1/2']`	`['1/2', '1/2']`	Passed
regression: random median 29	`['8', '8', '8']`	`['8', '8', '8']`	Passed
regression: random median 34	`['2', '2']`	`['2', '2']`	Passed
control: even kernel	`bad-kernel`	`bad-kernel`	Passed
control: even kernel four	`bad-kernel`	`bad-kernel`	Passed
control: random median 1	`['2', '3', '4', '-2']`	`['2', '3', '4', '-2']`	Passed
control: random median 3	`['2', '-3', '7', '8', '-2', '3', '8', '1']`	`['2', '-3', '7', '8', '-2', '3', '8', '1']`	Passed

SHA-256 / c51bda44783c92e3e40939ca27a72129ac93b817b05f0f695b82ddb4135c96c0

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 2026-09-29T14:51:36.264581+00:00.

Case digest / 1d232b03a55c5994a62aaf5d00b453e46be2cfe0747d96558ca7f8e426b5f18c