FA-91686 / Digital signal filters / Open access

Resampling plan sets the cutoff from the higher rate · case 01

Downsampling 48 kHz to 16 kHz keeps content up to 24 kHz, which aliases.

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ROOT CAUSE

The cutoff uses max(fin, fout) / 2.

VERIFIED REPAIR

Use min(fin, fout) / 2 times the rolloff.

Unsuccessful approach: The attempted repair always uses fout / 2, which is wrong when upsampling.

Case contract

Input [fin, fout, rolloff] (positive integer rates, rolloff in (0, 1]). Reduce fout/fin to up/down = L/M by gcd, intermediate rate = fin L, anti-alias cutoff = min(fin, fout)/2 * rolloff in Hz and normalized to the intermediate Nyquist. Return {"up", "down", "intermediate_rate", "cutoff_hz", "cutoff_norm"} or "bad-spec".

Why this case matters

Sample-rate converters are planned from these numbers; a wrong cutoff reference aliases or dulls the output.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(x):
    fin, fout, roll = x[0], x[1], Fraction(x[2])
    if fin <= 0 or fout <= 0 or not 0 < roll <= 1:
        return 'bad-spec'
    g = math.gcd(fin, fout)
    L, M = fout // g, fin // g
    inter = fin * L
    cutoff = Fraction(max(fin, fout), 2) * roll
    return {'up': L, 'down': M, 'intermediate_rate': inter, 'cutoff_hz': str(cutoff), 'cutoff_norm': str(cutoff / Fraction(inter, 2))}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: 48k to 44.1k', [48000, 44100, '9/10'], {'up': 147, 'down': 160, 'intermediate_rate': 7056000, 'cutoff_hz': '19845', 'cutoff_norm': '9/1600'}], ['regression: 44.1k to 48k', [44100, 48000, '9/10'], {'up': 160, 'down': 147, 'intermediate_rate': 7056000, 'cutoff_hz': '19845', 'cutoff_norm': '9/1600'}], ['regression: upsample by 2', [8000, 16000, '4/5'], {'up': 2, 'down': 1, 'intermediate_rate': 16000, 'cutoff_hz': '3200', 'cutoff_norm': '2/5'}], ['control: identity', [16000, 16000, '1'], {'up': 1, 'down': 1, 'intermediate_rate': 16000, 'cutoff_hz': '8000', 'cutoff_norm': '1'}], ['control: bad rolloff', [8000, 16000, '0'], 'bad-spec'], ['regression: downsample by 3', [48000, 16000, '1'], {'up': 1, 'down': 3, 'intermediate_rate': 48000, 'cutoff_hz': '8000', 'cutoff_norm': '1/3'}], ['regression: odd ratio', [22050, 32000, '19/20'], {'up': 640, 'down': 441, 'intermediate_rate': 14112000, 'cutoff_hz': '41895/4', 'cutoff_norm': '19/12800'}]], [['regression: upsample by 2', [8000, 16000, '4/5'], {'up': 2, 'down': 1, 'intermediate_rate': 16000, 'cutoff_hz': '3200', 'cutoff_norm': '2/5'}], ['regression: odd ratio', [22050, 32000, '19/20'], {'up': 640, 'down': 441, 'intermediate_rate': 14112000, 'cutoff_hz': '41895/4', 'cutoff_norm': '19/12800'}], ['regression: 44.1k to 48k', [44100, 48000, '9/10'], {'up': 160, 'down': 147, 'intermediate_rate': 7056000, 'cutoff_hz': '19845', 'cutoff_norm': '9/1600'}], ['control: identity', [16000, 16000, '1'], {'up': 1, 'down': 1, 'intermediate_rate': 16000, 'cutoff_hz': '8000', 'cutoff_norm': '1'}], ['control: bad rolloff', [8000, 16000, '0'], 'bad-spec'], ['regression: downsample by 3', [48000, 16000, '1'], {'up': 1, 'down': 3, 'intermediate_rate': 48000, 'cutoff_hz': '8000', 'cutoff_norm': '1/3'}], ['regression: coprime rates', [7, 5, '1/2'], {'up': 5, 'down': 7, 'intermediate_rate': 35, 'cutoff_hz': '5/4', 'cutoff_norm': '1/14'}]], [['regression: 48k to 44.1k', [48000, 44100, '9/10'], {'up': 147, 'down': 160, 'intermediate_rate': 7056000, 'cutoff_hz': '19845', 'cutoff_norm': '9/1600'}], ['regression: 44.1k to 48k', [44100, 48000, '9/10'], {'up': 160, 'down': 147, 'intermediate_rate': 7056000, 'cutoff_hz': '19845', 'cutoff_norm': '9/1600'}], ['regression: upsample by 2', [8000, 16000, '4/5'], {'up': 2, 'down': 1, 'intermediate_rate': 16000, 'cutoff_hz': '3200', 'cutoff_norm': '2/5'}], ['control: identity', [16000, 16000, '1'], {'up': 1, 'down': 1, 'intermediate_rate': 16000, 'cutoff_hz': '8000', 'cutoff_norm': '1'}], ['control: bad rolloff', [8000, 16000, '0'], 'bad-spec'], ['regression: odd ratio', [22050, 32000, '19/20'], {'up': 640, 'down': 441, 'intermediate_rate': 14112000, 'cutoff_hz': '41895/4', 'cutoff_norm': '19/12800'}], ['regression: coprime rates', [7, 5, '1/2'], {'up': 5, 'down': 7, 'intermediate_rate': 35, 'cutoff_hz': '5/4', 'cutoff_norm': '1/14'}]], [['regression: upsample by 2', [8000, 16000, '4/5'], {'up': 2, 'down': 1, 'intermediate_rate': 16000, 'cutoff_hz': '3200', 'cutoff_norm': '2/5'}], ['regression: odd ratio', [22050, 32000, '19/20'], {'up': 640, 'down': 441, 'intermediate_rate': 14112000, 'cutoff_hz': '41895/4', 'cutoff_norm': '19/12800'}], ['regression: 44.1k to 48k', [44100, 48000, '9/10'], {'up': 160, 'down': 147, 'intermediate_rate': 7056000, 'cutoff_hz': '19845', 'cutoff_norm': '9/1600'}], ['control: identity', [16000, 16000, '1'], {'up': 1, 'down': 1, 'intermediate_rate': 16000, 'cutoff_hz': '8000', 'cutoff_norm': '1'}], ['control: bad rolloff', [8000, 16000, '0'], 'bad-spec'], ['regression: coprime rates', [7, 5, '1/2'], {'up': 5, 'down': 7, 'intermediate_rate': 35, 'cutoff_hz': '5/4', 'cutoff_norm': '1/14'}], ['regression: 48k to 44.1k', [48000, 44100, '9/10'], {'up': 147, 'down': 160, 'intermediate_rate': 7056000, 'cutoff_hz': '19845', 'cutoff_norm': '9/1600'}]], [['regression: 48k to 44.1k', [48000, 44100, '9/10'], {'up': 147, 'down': 160, 'intermediate_rate': 7056000, 'cutoff_hz': '19845', 'cutoff_norm': '9/1600'}], ['regression: 44.1k to 48k', [44100, 48000, '9/10'], {'up': 160, 'down': 147, 'intermediate_rate': 7056000, 'cutoff_hz': '19845', 'cutoff_norm': '9/1600'}], ['regression: odd ratio', [22050, 32000, '19/20'], {'up': 640, 'down': 441, 'intermediate_rate': 14112000, 'cutoff_hz': '41895/4', 'cutoff_norm': '19/12800'}], ['control: identity', [16000, 16000, '1'], {'up': 1, 'down': 1, 'intermediate_rate': 16000, 'cutoff_hz': '8000', 'cutoff_norm': '1'}], ['control: bad rolloff', [8000, 16000, '0'], 'bad-spec'], ['regression: coprime rates', [7, 5, '1/2'], {'up': 5, 'down': 7, 'intermediate_rate': 35, 'cutoff_hz': '5/4', 'cutoff_norm': '1/14'}], ['regression: upsample by 2', [8000, 16000, '4/5'], {'up': 2, 'down': 1, 'intermediate_rate': 16000, 'cutoff_hz': '3200', 'cutoff_norm': '2/5'}]]]
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: 48k to 44.1k	`{'cutoff_hz': '21600', 'cutoff_norm': '3/490', 'down': 160, 'intermediate_rate': 7056000, 'up': 147}`	`{'cutoff_hz': '19845', 'cutoff_norm': '9/1600', 'down': 160, 'intermediate_rate': 7056000, 'up': 147}`	Failed
regression: 44.1k to 48k	`{'cutoff_hz': '21600', 'cutoff_norm': '3/490', 'down': 147, 'intermediate_rate': 7056000, 'up': 160}`	`{'cutoff_hz': '19845', 'cutoff_norm': '9/1600', 'down': 147, 'intermediate_rate': 7056000, 'up': 160}`	Failed
regression: upsample by 2	`{'cutoff_hz': '6400', 'cutoff_norm': '4/5', 'down': 1, 'intermediate_rate': 16000, 'up': 2}`	`{'cutoff_hz': '3200', 'cutoff_norm': '2/5', 'down': 1, 'intermediate_rate': 16000, 'up': 2}`	Failed
control: identity	`{'cutoff_hz': '8000', 'cutoff_norm': '1', 'down': 1, 'intermediate_rate': 16000, 'up': 1}`	`{'cutoff_hz': '8000', 'cutoff_norm': '1', 'down': 1, 'intermediate_rate': 16000, 'up': 1}`	Passed
control: bad rolloff	`bad-spec`	`bad-spec`	Passed
regression: downsample by 3	`{'cutoff_hz': '24000', 'cutoff_norm': '1', 'down': 3, 'intermediate_rate': 48000, 'up': 1}`	`{'cutoff_hz': '8000', 'cutoff_norm': '1/3', 'down': 3, 'intermediate_rate': 48000, 'up': 1}`	Failed
regression: odd ratio	`{'cutoff_hz': '15200', 'cutoff_norm': '19/8820', 'down': 441, 'intermediate_rate': 14112000, 'up': 640}`	`{'cutoff_hz': '41895/4', 'cutoff_norm': '19/12800', 'down': 441, 'intermediate_rate': 14112000, 'up': 640}`	Failed

SHA-256 / 0e465b206f1ceddebcec5f4643d91689941612c61ca3189d07b43d8c6ab13a94

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(x):
    fin, fout, roll = x[0], x[1], Fraction(x[2])
    if fin <= 0 or fout <= 0 or not 0 < roll <= 1:
        return 'bad-spec'
    g = math.gcd(fin, fout)
    L, M = fout // g, fin // g
    inter = fin * L
    cutoff = Fraction(fout, 2) * roll
    return {'up': L, 'down': M, 'intermediate_rate': inter, 'cutoff_hz': str(cutoff), 'cutoff_norm': str(cutoff / Fraction(inter, 2))}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: 48k to 44.1k', [48000, 44100, '9/10'], {'up': 147, 'down': 160, 'intermediate_rate': 7056000, 'cutoff_hz': '19845', 'cutoff_norm': '9/1600'}], ['regression: 44.1k to 48k', [44100, 48000, '9/10'], {'up': 160, 'down': 147, 'intermediate_rate': 7056000, 'cutoff_hz': '19845', 'cutoff_norm': '9/1600'}], ['regression: upsample by 2', [8000, 16000, '4/5'], {'up': 2, 'down': 1, 'intermediate_rate': 16000, 'cutoff_hz': '3200', 'cutoff_norm': '2/5'}], ['control: identity', [16000, 16000, '1'], {'up': 1, 'down': 1, 'intermediate_rate': 16000, 'cutoff_hz': '8000', 'cutoff_norm': '1'}], ['control: bad rolloff', [8000, 16000, '0'], 'bad-spec'], ['regression: downsample by 3', [48000, 16000, '1'], {'up': 1, 'down': 3, 'intermediate_rate': 48000, 'cutoff_hz': '8000', 'cutoff_norm': '1/3'}], ['regression: odd ratio', [22050, 32000, '19/20'], {'up': 640, 'down': 441, 'intermediate_rate': 14112000, 'cutoff_hz': '41895/4', 'cutoff_norm': '19/12800'}]], [['regression: upsample by 2', [8000, 16000, '4/5'], {'up': 2, 'down': 1, 'intermediate_rate': 16000, 'cutoff_hz': '3200', 'cutoff_norm': '2/5'}], ['regression: odd ratio', [22050, 32000, '19/20'], {'up': 640, 'down': 441, 'intermediate_rate': 14112000, 'cutoff_hz': '41895/4', 'cutoff_norm': '19/12800'}], ['regression: 44.1k to 48k', [44100, 48000, '9/10'], {'up': 160, 'down': 147, 'intermediate_rate': 7056000, 'cutoff_hz': '19845', 'cutoff_norm': '9/1600'}], ['control: identity', [16000, 16000, '1'], {'up': 1, 'down': 1, 'intermediate_rate': 16000, 'cutoff_hz': '8000', 'cutoff_norm': '1'}], ['control: bad rolloff', [8000, 16000, '0'], 'bad-spec'], ['regression: downsample by 3', [48000, 16000, '1'], {'up': 1, 'down': 3, 'intermediate_rate': 48000, 'cutoff_hz': '8000', 'cutoff_norm': '1/3'}], ['regression: coprime rates', [7, 5, '1/2'], {'up': 5, 'down': 7, 'intermediate_rate': 35, 'cutoff_hz': '5/4', 'cutoff_norm': '1/14'}]], [['regression: 48k to 44.1k', [48000, 44100, '9/10'], {'up': 147, 'down': 160, 'intermediate_rate': 7056000, 'cutoff_hz': '19845', 'cutoff_norm': '9/1600'}], ['regression: 44.1k to 48k', [44100, 48000, '9/10'], {'up': 160, 'down': 147, 'intermediate_rate': 7056000, 'cutoff_hz': '19845', 'cutoff_norm': '9/1600'}], ['regression: upsample by 2', [8000, 16000, '4/5'], {'up': 2, 'down': 1, 'intermediate_rate': 16000, 'cutoff_hz': '3200', 'cutoff_norm': '2/5'}], ['control: identity', [16000, 16000, '1'], {'up': 1, 'down': 1, 'intermediate_rate': 16000, 'cutoff_hz': '8000', 'cutoff_norm': '1'}], ['control: bad rolloff', [8000, 16000, '0'], 'bad-spec'], ['regression: odd ratio', [22050, 32000, '19/20'], {'up': 640, 'down': 441, 'intermediate_rate': 14112000, 'cutoff_hz': '41895/4', 'cutoff_norm': '19/12800'}], ['regression: coprime rates', [7, 5, '1/2'], {'up': 5, 'down': 7, 'intermediate_rate': 35, 'cutoff_hz': '5/4', 'cutoff_norm': '1/14'}]], [['regression: upsample by 2', [8000, 16000, '4/5'], {'up': 2, 'down': 1, 'intermediate_rate': 16000, 'cutoff_hz': '3200', 'cutoff_norm': '2/5'}], ['regression: odd ratio', [22050, 32000, '19/20'], {'up': 640, 'down': 441, 'intermediate_rate': 14112000, 'cutoff_hz': '41895/4', 'cutoff_norm': '19/12800'}], ['regression: 44.1k to 48k', [44100, 48000, '9/10'], {'up': 160, 'down': 147, 'intermediate_rate': 7056000, 'cutoff_hz': '19845', 'cutoff_norm': '9/1600'}], ['control: identity', [16000, 16000, '1'], {'up': 1, 'down': 1, 'intermediate_rate': 16000, 'cutoff_hz': '8000', 'cutoff_norm': '1'}], ['control: bad rolloff', [8000, 16000, '0'], 'bad-spec'], ['regression: coprime rates', [7, 5, '1/2'], {'up': 5, 'down': 7, 'intermediate_rate': 35, 'cutoff_hz': '5/4', 'cutoff_norm': '1/14'}], ['regression: 48k to 44.1k', [48000, 44100, '9/10'], {'up': 147, 'down': 160, 'intermediate_rate': 7056000, 'cutoff_hz': '19845', 'cutoff_norm': '9/1600'}]], [['regression: 48k to 44.1k', [48000, 44100, '9/10'], {'up': 147, 'down': 160, 'intermediate_rate': 7056000, 'cutoff_hz': '19845', 'cutoff_norm': '9/1600'}], ['regression: 44.1k to 48k', [44100, 48000, '9/10'], {'up': 160, 'down': 147, 'intermediate_rate': 7056000, 'cutoff_hz': '19845', 'cutoff_norm': '9/1600'}], ['regression: odd ratio', [22050, 32000, '19/20'], {'up': 640, 'down': 441, 'intermediate_rate': 14112000, 'cutoff_hz': '41895/4', 'cutoff_norm': '19/12800'}], ['control: identity', [16000, 16000, '1'], {'up': 1, 'down': 1, 'intermediate_rate': 16000, 'cutoff_hz': '8000', 'cutoff_norm': '1'}], ['control: bad rolloff', [8000, 16000, '0'], 'bad-spec'], ['regression: coprime rates', [7, 5, '1/2'], {'up': 5, 'down': 7, 'intermediate_rate': 35, 'cutoff_hz': '5/4', 'cutoff_norm': '1/14'}], ['regression: upsample by 2', [8000, 16000, '4/5'], {'up': 2, 'down': 1, 'intermediate_rate': 16000, 'cutoff_hz': '3200', 'cutoff_norm': '2/5'}]]]
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: 48k to 44.1k	`{'cutoff_hz': '19845', 'cutoff_norm': '9/1600', 'down': 160, 'intermediate_rate': 7056000, 'up': 147}`	`{'cutoff_hz': '19845', 'cutoff_norm': '9/1600', 'down': 160, 'intermediate_rate': 7056000, 'up': 147}`	Passed
regression: 44.1k to 48k	`{'cutoff_hz': '21600', 'cutoff_norm': '3/490', 'down': 147, 'intermediate_rate': 7056000, 'up': 160}`	`{'cutoff_hz': '19845', 'cutoff_norm': '9/1600', 'down': 147, 'intermediate_rate': 7056000, 'up': 160}`	Failed
regression: upsample by 2	`{'cutoff_hz': '6400', 'cutoff_norm': '4/5', 'down': 1, 'intermediate_rate': 16000, 'up': 2}`	`{'cutoff_hz': '3200', 'cutoff_norm': '2/5', 'down': 1, 'intermediate_rate': 16000, 'up': 2}`	Failed
control: identity	`{'cutoff_hz': '8000', 'cutoff_norm': '1', 'down': 1, 'intermediate_rate': 16000, 'up': 1}`	`{'cutoff_hz': '8000', 'cutoff_norm': '1', 'down': 1, 'intermediate_rate': 16000, 'up': 1}`	Passed
control: bad rolloff	`bad-spec`	`bad-spec`	Passed
regression: downsample by 3	`{'cutoff_hz': '8000', 'cutoff_norm': '1/3', 'down': 3, 'intermediate_rate': 48000, 'up': 1}`	`{'cutoff_hz': '8000', 'cutoff_norm': '1/3', 'down': 3, 'intermediate_rate': 48000, 'up': 1}`	Passed
regression: odd ratio	`{'cutoff_hz': '15200', 'cutoff_norm': '19/8820', 'down': 441, 'intermediate_rate': 14112000, 'up': 640}`	`{'cutoff_hz': '41895/4', 'cutoff_norm': '19/12800', 'down': 441, 'intermediate_rate': 14112000, 'up': 640}`	Failed

SHA-256 / 6a507196c030b49d60dd1005e6167fcb2455df8e38cdc32daac9714cc1942a85

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(x):
    fin, fout, roll = x[0], x[1], Fraction(x[2])
    if fin <= 0 or fout <= 0 or not 0 < roll <= 1:
        return 'bad-spec'
    g = math.gcd(fin, fout)
    L, M = fout // g, fin // g
    inter = fin * L
    cutoff = Fraction(min(fin, fout), 2) * roll
    return {'up': L, 'down': M, 'intermediate_rate': inter, 'cutoff_hz': str(cutoff), 'cutoff_norm': str(cutoff / Fraction(inter, 2))}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: 48k to 44.1k', [48000, 44100, '9/10'], {'up': 147, 'down': 160, 'intermediate_rate': 7056000, 'cutoff_hz': '19845', 'cutoff_norm': '9/1600'}], ['regression: 44.1k to 48k', [44100, 48000, '9/10'], {'up': 160, 'down': 147, 'intermediate_rate': 7056000, 'cutoff_hz': '19845', 'cutoff_norm': '9/1600'}], ['regression: upsample by 2', [8000, 16000, '4/5'], {'up': 2, 'down': 1, 'intermediate_rate': 16000, 'cutoff_hz': '3200', 'cutoff_norm': '2/5'}], ['control: identity', [16000, 16000, '1'], {'up': 1, 'down': 1, 'intermediate_rate': 16000, 'cutoff_hz': '8000', 'cutoff_norm': '1'}], ['control: bad rolloff', [8000, 16000, '0'], 'bad-spec'], ['regression: downsample by 3', [48000, 16000, '1'], {'up': 1, 'down': 3, 'intermediate_rate': 48000, 'cutoff_hz': '8000', 'cutoff_norm': '1/3'}], ['regression: odd ratio', [22050, 32000, '19/20'], {'up': 640, 'down': 441, 'intermediate_rate': 14112000, 'cutoff_hz': '41895/4', 'cutoff_norm': '19/12800'}]], [['regression: upsample by 2', [8000, 16000, '4/5'], {'up': 2, 'down': 1, 'intermediate_rate': 16000, 'cutoff_hz': '3200', 'cutoff_norm': '2/5'}], ['regression: odd ratio', [22050, 32000, '19/20'], {'up': 640, 'down': 441, 'intermediate_rate': 14112000, 'cutoff_hz': '41895/4', 'cutoff_norm': '19/12800'}], ['regression: 44.1k to 48k', [44100, 48000, '9/10'], {'up': 160, 'down': 147, 'intermediate_rate': 7056000, 'cutoff_hz': '19845', 'cutoff_norm': '9/1600'}], ['control: identity', [16000, 16000, '1'], {'up': 1, 'down': 1, 'intermediate_rate': 16000, 'cutoff_hz': '8000', 'cutoff_norm': '1'}], ['control: bad rolloff', [8000, 16000, '0'], 'bad-spec'], ['regression: downsample by 3', [48000, 16000, '1'], {'up': 1, 'down': 3, 'intermediate_rate': 48000, 'cutoff_hz': '8000', 'cutoff_norm': '1/3'}], ['regression: coprime rates', [7, 5, '1/2'], {'up': 5, 'down': 7, 'intermediate_rate': 35, 'cutoff_hz': '5/4', 'cutoff_norm': '1/14'}]], [['regression: 48k to 44.1k', [48000, 44100, '9/10'], {'up': 147, 'down': 160, 'intermediate_rate': 7056000, 'cutoff_hz': '19845', 'cutoff_norm': '9/1600'}], ['regression: 44.1k to 48k', [44100, 48000, '9/10'], {'up': 160, 'down': 147, 'intermediate_rate': 7056000, 'cutoff_hz': '19845', 'cutoff_norm': '9/1600'}], ['regression: upsample by 2', [8000, 16000, '4/5'], {'up': 2, 'down': 1, 'intermediate_rate': 16000, 'cutoff_hz': '3200', 'cutoff_norm': '2/5'}], ['control: identity', [16000, 16000, '1'], {'up': 1, 'down': 1, 'intermediate_rate': 16000, 'cutoff_hz': '8000', 'cutoff_norm': '1'}], ['control: bad rolloff', [8000, 16000, '0'], 'bad-spec'], ['regression: odd ratio', [22050, 32000, '19/20'], {'up': 640, 'down': 441, 'intermediate_rate': 14112000, 'cutoff_hz': '41895/4', 'cutoff_norm': '19/12800'}], ['regression: coprime rates', [7, 5, '1/2'], {'up': 5, 'down': 7, 'intermediate_rate': 35, 'cutoff_hz': '5/4', 'cutoff_norm': '1/14'}]], [['regression: upsample by 2', [8000, 16000, '4/5'], {'up': 2, 'down': 1, 'intermediate_rate': 16000, 'cutoff_hz': '3200', 'cutoff_norm': '2/5'}], ['regression: odd ratio', [22050, 32000, '19/20'], {'up': 640, 'down': 441, 'intermediate_rate': 14112000, 'cutoff_hz': '41895/4', 'cutoff_norm': '19/12800'}], ['regression: 44.1k to 48k', [44100, 48000, '9/10'], {'up': 160, 'down': 147, 'intermediate_rate': 7056000, 'cutoff_hz': '19845', 'cutoff_norm': '9/1600'}], ['control: identity', [16000, 16000, '1'], {'up': 1, 'down': 1, 'intermediate_rate': 16000, 'cutoff_hz': '8000', 'cutoff_norm': '1'}], ['control: bad rolloff', [8000, 16000, '0'], 'bad-spec'], ['regression: coprime rates', [7, 5, '1/2'], {'up': 5, 'down': 7, 'intermediate_rate': 35, 'cutoff_hz': '5/4', 'cutoff_norm': '1/14'}], ['regression: 48k to 44.1k', [48000, 44100, '9/10'], {'up': 147, 'down': 160, 'intermediate_rate': 7056000, 'cutoff_hz': '19845', 'cutoff_norm': '9/1600'}]], [['regression: 48k to 44.1k', [48000, 44100, '9/10'], {'up': 147, 'down': 160, 'intermediate_rate': 7056000, 'cutoff_hz': '19845', 'cutoff_norm': '9/1600'}], ['regression: 44.1k to 48k', [44100, 48000, '9/10'], {'up': 160, 'down': 147, 'intermediate_rate': 7056000, 'cutoff_hz': '19845', 'cutoff_norm': '9/1600'}], ['regression: odd ratio', [22050, 32000, '19/20'], {'up': 640, 'down': 441, 'intermediate_rate': 14112000, 'cutoff_hz': '41895/4', 'cutoff_norm': '19/12800'}], ['control: identity', [16000, 16000, '1'], {'up': 1, 'down': 1, 'intermediate_rate': 16000, 'cutoff_hz': '8000', 'cutoff_norm': '1'}], ['control: bad rolloff', [8000, 16000, '0'], 'bad-spec'], ['regression: coprime rates', [7, 5, '1/2'], {'up': 5, 'down': 7, 'intermediate_rate': 35, 'cutoff_hz': '5/4', 'cutoff_norm': '1/14'}], ['regression: upsample by 2', [8000, 16000, '4/5'], {'up': 2, 'down': 1, 'intermediate_rate': 16000, 'cutoff_hz': '3200', 'cutoff_norm': '2/5'}]]]
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: 48k to 44.1k	`{'cutoff_hz': '19845', 'cutoff_norm': '9/1600', 'down': 160, 'intermediate_rate': 7056000, 'up': 147}`	`{'cutoff_hz': '19845', 'cutoff_norm': '9/1600', 'down': 160, 'intermediate_rate': 7056000, 'up': 147}`	Passed
regression: 44.1k to 48k	`{'cutoff_hz': '19845', 'cutoff_norm': '9/1600', 'down': 147, 'intermediate_rate': 7056000, 'up': 160}`	`{'cutoff_hz': '19845', 'cutoff_norm': '9/1600', 'down': 147, 'intermediate_rate': 7056000, 'up': 160}`	Passed
regression: upsample by 2	`{'cutoff_hz': '3200', 'cutoff_norm': '2/5', 'down': 1, 'intermediate_rate': 16000, 'up': 2}`	`{'cutoff_hz': '3200', 'cutoff_norm': '2/5', 'down': 1, 'intermediate_rate': 16000, 'up': 2}`	Passed
control: identity	`{'cutoff_hz': '8000', 'cutoff_norm': '1', 'down': 1, 'intermediate_rate': 16000, 'up': 1}`	`{'cutoff_hz': '8000', 'cutoff_norm': '1', 'down': 1, 'intermediate_rate': 16000, 'up': 1}`	Passed
control: bad rolloff	`bad-spec`	`bad-spec`	Passed
regression: downsample by 3	`{'cutoff_hz': '8000', 'cutoff_norm': '1/3', 'down': 3, 'intermediate_rate': 48000, 'up': 1}`	`{'cutoff_hz': '8000', 'cutoff_norm': '1/3', 'down': 3, 'intermediate_rate': 48000, 'up': 1}`	Passed
regression: odd ratio	`{'cutoff_hz': '41895/4', 'cutoff_norm': '19/12800', 'down': 441, 'intermediate_rate': 14112000, 'up': 640}`	`{'cutoff_hz': '41895/4', 'cutoff_norm': '19/12800', 'down': 441, 'intermediate_rate': 14112000, 'up': 640}`	Passed

SHA-256 / 6c17f9eeb9594800427783a9e34bbc32b209c3ff222187cbc9afa1cf1131fade

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 2026-09-29T14:51:38.238831+00:00.

Case digest / 167beabbf154a9793bc2d2c453a2414ce6c7c5f8998006d5fc69ddc23e38d6eb