FA-91711 / Digital signal filters / Open access
Bilinear highpass places its zero at Nyquist · case 01
The "highpass" blocks high frequencies and passes DC.
ROOT CAUSE
b1 is +K/(K+wc), giving a zero at z = -1 instead of z = 1.
VERIFIED REPAIR
Use b = [K/d, -K/d].
Unsuccessful approach: The attempted repair uses -wc/d for b1, which does not place the zero at DC.
Case contract
Input [kind, wc, fs] with rational analog cutoff wc (rad/s) and sample rate fs. Map H(s) = wc/(s+wc) (lowpass) or s/(s+wc) (highpass) with s = K (1 - z^-1)/(1 + z^-1), K = 2 fs, no prewarping. Return {"b": [b0, b1], "a": [1, a1]} as fraction strings normalized so a0 = 1, or "bad-spec".
Why this case matters
The bilinear transform is the standard analog-to-digital mapping; K or sign slips move the cutoff or flip the filter type.
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):
kind, wc, fs = x[0], Fraction(x[1]), Fraction(x[2])
if wc <= 0 or fs <= 0:
return 'bad-spec'
K = 2 * fs
d = K + wc
if kind == 'lowpass':
b = [wc / d, wc / d]
else:
b = [K / d, K / d]
a = [Fraction(1), (wc - K) / d]
return {'b': [str(v) for v in b], 'a': [str(v) for v in a]}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: highpass wc=100 fs=1000', ['highpass', '100', '1000'], {'b': ['20/21', '-20/21'], 'a': ['1', '-19/21']}], ['regression: highpass wc=1 fs=1', ['highpass', '1', '1'], {'b': ['2/3', '-2/3'], 'a': ['1', '-1/3']}], ['regression: highpass wc=3 fs=1/2', ['highpass', '3', '1/2'], {'b': ['1/4', '-1/4'], 'a': ['1', '1/2']}], ['control: lowpass wc=100 fs=1000', ['lowpass', '100', '1000'], {'b': ['1/21', '1/21'], 'a': ['1', '-19/21']}], ['control: lowpass wc=1 fs=1', ['lowpass', '1', '1'], {'b': ['1/3', '1/3'], 'a': ['1', '-1/3']}], ['control: lowpass wc=3 fs=1/2', ['lowpass', '3', '1/2'], {'b': ['3/4', '3/4'], 'a': ['1', '1/2']}], ['control: lowpass wc=2000 fs=48000', ['lowpass', '2000', '48000'], {'b': ['1/49', '1/49'], 'a': ['1', '-47/49']}]], [['regression: highpass wc=2000 fs=48000', ['highpass', '2000', '48000'], {'b': ['48/49', '-48/49'], 'a': ['1', '-47/49']}], ['regression: highpass wc=1/2 fs=2', ['highpass', '1/2', '2'], {'b': ['8/9', '-8/9'], 'a': ['1', '-7/9']}], ['regression: highpass wc=3 fs=1/2', ['highpass', '3', '1/2'], {'b': ['1/4', '-1/4'], 'a': ['1', '1/2']}], ['control: lowpass wc=1/2 fs=2', ['lowpass', '1/2', '2'], {'b': ['1/9', '1/9'], 'a': ['1', '-7/9']}], ['control: bad spec', ['lowpass', '0', '1'], 'bad-spec'], ['control: lowpass wc=100 fs=1000', ['lowpass', '100', '1000'], {'b': ['1/21', '1/21'], 'a': ['1', '-19/21']}], ['control: lowpass wc=1 fs=1', ['lowpass', '1', '1'], {'b': ['1/3', '1/3'], 'a': ['1', '-1/3']}]], [['regression: highpass wc=1 fs=1', ['highpass', '1', '1'], {'b': ['2/3', '-2/3'], 'a': ['1', '-1/3']}], ['regression: highpass wc=3 fs=1/2', ['highpass', '3', '1/2'], {'b': ['1/4', '-1/4'], 'a': ['1', '1/2']}], ['regression: highpass wc=1/2 fs=2', ['highpass', '1/2', '2'], {'b': ['8/9', '-8/9'], 'a': ['1', '-7/9']}], ['control: lowpass wc=3 fs=1/2', ['lowpass', '3', '1/2'], {'b': ['3/4', '3/4'], 'a': ['1', '1/2']}], ['control: lowpass wc=2000 fs=48000', ['lowpass', '2000', '48000'], {'b': ['1/49', '1/49'], 'a': ['1', '-47/49']}], ['control: lowpass wc=1/2 fs=2', ['lowpass', '1/2', '2'], {'b': ['1/9', '1/9'], 'a': ['1', '-7/9']}], ['control: bad spec', ['lowpass', '0', '1'], 'bad-spec']], [['regression: highpass wc=1/2 fs=2', ['highpass', '1/2', '2'], {'b': ['8/9', '-8/9'], 'a': ['1', '-7/9']}], ['regression: highpass wc=100 fs=1000', ['highpass', '100', '1000'], {'b': ['20/21', '-20/21'], 'a': ['1', '-19/21']}], ['regression: highpass wc=1 fs=1', ['highpass', '1', '1'], {'b': ['2/3', '-2/3'], 'a': ['1', '-1/3']}], ['control: lowpass wc=100 fs=1000', ['lowpass', '100', '1000'], {'b': ['1/21', '1/21'], 'a': ['1', '-19/21']}], ['control: lowpass wc=1 fs=1', ['lowpass', '1', '1'], {'b': ['1/3', '1/3'], 'a': ['1', '-1/3']}], ['control: lowpass wc=3 fs=1/2', ['lowpass', '3', '1/2'], {'b': ['3/4', '3/4'], 'a': ['1', '1/2']}], ['control: lowpass wc=2000 fs=48000', ['lowpass', '2000', '48000'], {'b': ['1/49', '1/49'], 'a': ['1', '-47/49']}]], [['regression: highpass wc=3 fs=1/2', ['highpass', '3', '1/2'], {'b': ['1/4', '-1/4'], 'a': ['1', '1/2']}], ['regression: highpass wc=2000 fs=48000', ['highpass', '2000', '48000'], {'b': ['48/49', '-48/49'], 'a': ['1', '-47/49']}], ['regression: highpass wc=1/2 fs=2', ['highpass', '1/2', '2'], {'b': ['8/9', '-8/9'], 'a': ['1', '-7/9']}], ['control: lowpass wc=1/2 fs=2', ['lowpass', '1/2', '2'], {'b': ['1/9', '1/9'], 'a': ['1', '-7/9']}], ['control: bad spec', ['lowpass', '0', '1'], 'bad-spec'], ['control: lowpass wc=100 fs=1000', ['lowpass', '100', '1000'], {'b': ['1/21', '1/21'], 'a': ['1', '-19/21']}], ['control: lowpass wc=1 fs=1', ['lowpass', '1', '1'], {'b': ['1/3', '1/3'], 'a': ['1', '-1/3']}]]]
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: highpass wc=100 fs=1000 | {'a': ['1', '-19/21'], 'b': ['20/21', '20/21']} | {'a': ['1', '-19/21'], 'b': ['20/21', '-20/21']} | Failed |
| regression: highpass wc=1 fs=1 | {'a': ['1', '-1/3'], 'b': ['2/3', '2/3']} | {'a': ['1', '-1/3'], 'b': ['2/3', '-2/3']} | Failed |
| regression: highpass wc=3 fs=1/2 | {'a': ['1', '1/2'], 'b': ['1/4', '1/4']} | {'a': ['1', '1/2'], 'b': ['1/4', '-1/4']} | Failed |
| control: lowpass wc=100 fs=1000 | {'a': ['1', '-19/21'], 'b': ['1/21', '1/21']} | {'a': ['1', '-19/21'], 'b': ['1/21', '1/21']} | Passed |
| control: lowpass wc=1 fs=1 | {'a': ['1', '-1/3'], 'b': ['1/3', '1/3']} | {'a': ['1', '-1/3'], 'b': ['1/3', '1/3']} | Passed |
| control: lowpass wc=3 fs=1/2 | {'a': ['1', '1/2'], 'b': ['3/4', '3/4']} | {'a': ['1', '1/2'], 'b': ['3/4', '3/4']} | Passed |
| control: lowpass wc=2000 fs=48000 | {'a': ['1', '-47/49'], 'b': ['1/49', '1/49']} | {'a': ['1', '-47/49'], 'b': ['1/49', '1/49']} | Passed |
SHA-256 / ddb2212213089ebab11795fffeeab1bcf6585122f424c9302299bc6148eaa2f4
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):
kind, wc, fs = x[0], Fraction(x[1]), Fraction(x[2])
if wc <= 0 or fs <= 0:
return 'bad-spec'
K = 2 * fs
d = K + wc
if kind == 'lowpass':
b = [wc / d, wc / d]
else:
b = [K / d, -wc / d]
a = [Fraction(1), (wc - K) / d]
return {'b': [str(v) for v in b], 'a': [str(v) for v in a]}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: highpass wc=100 fs=1000', ['highpass', '100', '1000'], {'b': ['20/21', '-20/21'], 'a': ['1', '-19/21']}], ['regression: highpass wc=1 fs=1', ['highpass', '1', '1'], {'b': ['2/3', '-2/3'], 'a': ['1', '-1/3']}], ['regression: highpass wc=3 fs=1/2', ['highpass', '3', '1/2'], {'b': ['1/4', '-1/4'], 'a': ['1', '1/2']}], ['control: lowpass wc=100 fs=1000', ['lowpass', '100', '1000'], {'b': ['1/21', '1/21'], 'a': ['1', '-19/21']}], ['control: lowpass wc=1 fs=1', ['lowpass', '1', '1'], {'b': ['1/3', '1/3'], 'a': ['1', '-1/3']}], ['control: lowpass wc=3 fs=1/2', ['lowpass', '3', '1/2'], {'b': ['3/4', '3/4'], 'a': ['1', '1/2']}], ['control: lowpass wc=2000 fs=48000', ['lowpass', '2000', '48000'], {'b': ['1/49', '1/49'], 'a': ['1', '-47/49']}]], [['regression: highpass wc=2000 fs=48000', ['highpass', '2000', '48000'], {'b': ['48/49', '-48/49'], 'a': ['1', '-47/49']}], ['regression: highpass wc=1/2 fs=2', ['highpass', '1/2', '2'], {'b': ['8/9', '-8/9'], 'a': ['1', '-7/9']}], ['regression: highpass wc=3 fs=1/2', ['highpass', '3', '1/2'], {'b': ['1/4', '-1/4'], 'a': ['1', '1/2']}], ['control: lowpass wc=1/2 fs=2', ['lowpass', '1/2', '2'], {'b': ['1/9', '1/9'], 'a': ['1', '-7/9']}], ['control: bad spec', ['lowpass', '0', '1'], 'bad-spec'], ['control: lowpass wc=100 fs=1000', ['lowpass', '100', '1000'], {'b': ['1/21', '1/21'], 'a': ['1', '-19/21']}], ['control: lowpass wc=1 fs=1', ['lowpass', '1', '1'], {'b': ['1/3', '1/3'], 'a': ['1', '-1/3']}]], [['regression: highpass wc=1 fs=1', ['highpass', '1', '1'], {'b': ['2/3', '-2/3'], 'a': ['1', '-1/3']}], ['regression: highpass wc=3 fs=1/2', ['highpass', '3', '1/2'], {'b': ['1/4', '-1/4'], 'a': ['1', '1/2']}], ['regression: highpass wc=1/2 fs=2', ['highpass', '1/2', '2'], {'b': ['8/9', '-8/9'], 'a': ['1', '-7/9']}], ['control: lowpass wc=3 fs=1/2', ['lowpass', '3', '1/2'], {'b': ['3/4', '3/4'], 'a': ['1', '1/2']}], ['control: lowpass wc=2000 fs=48000', ['lowpass', '2000', '48000'], {'b': ['1/49', '1/49'], 'a': ['1', '-47/49']}], ['control: lowpass wc=1/2 fs=2', ['lowpass', '1/2', '2'], {'b': ['1/9', '1/9'], 'a': ['1', '-7/9']}], ['control: bad spec', ['lowpass', '0', '1'], 'bad-spec']], [['regression: highpass wc=1/2 fs=2', ['highpass', '1/2', '2'], {'b': ['8/9', '-8/9'], 'a': ['1', '-7/9']}], ['regression: highpass wc=100 fs=1000', ['highpass', '100', '1000'], {'b': ['20/21', '-20/21'], 'a': ['1', '-19/21']}], ['regression: highpass wc=1 fs=1', ['highpass', '1', '1'], {'b': ['2/3', '-2/3'], 'a': ['1', '-1/3']}], ['control: lowpass wc=100 fs=1000', ['lowpass', '100', '1000'], {'b': ['1/21', '1/21'], 'a': ['1', '-19/21']}], ['control: lowpass wc=1 fs=1', ['lowpass', '1', '1'], {'b': ['1/3', '1/3'], 'a': ['1', '-1/3']}], ['control: lowpass wc=3 fs=1/2', ['lowpass', '3', '1/2'], {'b': ['3/4', '3/4'], 'a': ['1', '1/2']}], ['control: lowpass wc=2000 fs=48000', ['lowpass', '2000', '48000'], {'b': ['1/49', '1/49'], 'a': ['1', '-47/49']}]], [['regression: highpass wc=3 fs=1/2', ['highpass', '3', '1/2'], {'b': ['1/4', '-1/4'], 'a': ['1', '1/2']}], ['regression: highpass wc=2000 fs=48000', ['highpass', '2000', '48000'], {'b': ['48/49', '-48/49'], 'a': ['1', '-47/49']}], ['regression: highpass wc=1/2 fs=2', ['highpass', '1/2', '2'], {'b': ['8/9', '-8/9'], 'a': ['1', '-7/9']}], ['control: lowpass wc=1/2 fs=2', ['lowpass', '1/2', '2'], {'b': ['1/9', '1/9'], 'a': ['1', '-7/9']}], ['control: bad spec', ['lowpass', '0', '1'], 'bad-spec'], ['control: lowpass wc=100 fs=1000', ['lowpass', '100', '1000'], {'b': ['1/21', '1/21'], 'a': ['1', '-19/21']}], ['control: lowpass wc=1 fs=1', ['lowpass', '1', '1'], {'b': ['1/3', '1/3'], 'a': ['1', '-1/3']}]]]
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: highpass wc=100 fs=1000 | {'a': ['1', '-19/21'], 'b': ['20/21', '-1/21']} | {'a': ['1', '-19/21'], 'b': ['20/21', '-20/21']} | Failed |
| regression: highpass wc=1 fs=1 | {'a': ['1', '-1/3'], 'b': ['2/3', '-1/3']} | {'a': ['1', '-1/3'], 'b': ['2/3', '-2/3']} | Failed |
| regression: highpass wc=3 fs=1/2 | {'a': ['1', '1/2'], 'b': ['1/4', '-3/4']} | {'a': ['1', '1/2'], 'b': ['1/4', '-1/4']} | Failed |
| control: lowpass wc=100 fs=1000 | {'a': ['1', '-19/21'], 'b': ['1/21', '1/21']} | {'a': ['1', '-19/21'], 'b': ['1/21', '1/21']} | Passed |
| control: lowpass wc=1 fs=1 | {'a': ['1', '-1/3'], 'b': ['1/3', '1/3']} | {'a': ['1', '-1/3'], 'b': ['1/3', '1/3']} | Passed |
| control: lowpass wc=3 fs=1/2 | {'a': ['1', '1/2'], 'b': ['3/4', '3/4']} | {'a': ['1', '1/2'], 'b': ['3/4', '3/4']} | Passed |
| control: lowpass wc=2000 fs=48000 | {'a': ['1', '-47/49'], 'b': ['1/49', '1/49']} | {'a': ['1', '-47/49'], 'b': ['1/49', '1/49']} | Passed |
SHA-256 / 9be1288d7605b43f64213fb4d3c01b7cc90b261794edb5a352d9daabbcb823f3
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):
kind, wc, fs = x[0], Fraction(x[1]), Fraction(x[2])
if wc <= 0 or fs <= 0:
return 'bad-spec'
K = 2 * fs
d = K + wc
if kind == 'lowpass':
b = [wc / d, wc / d]
else:
b = [K / d, -K / d]
a = [Fraction(1), (wc - K) / d]
return {'b': [str(v) for v in b], 'a': [str(v) for v in a]}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: highpass wc=100 fs=1000', ['highpass', '100', '1000'], {'b': ['20/21', '-20/21'], 'a': ['1', '-19/21']}], ['regression: highpass wc=1 fs=1', ['highpass', '1', '1'], {'b': ['2/3', '-2/3'], 'a': ['1', '-1/3']}], ['regression: highpass wc=3 fs=1/2', ['highpass', '3', '1/2'], {'b': ['1/4', '-1/4'], 'a': ['1', '1/2']}], ['control: lowpass wc=100 fs=1000', ['lowpass', '100', '1000'], {'b': ['1/21', '1/21'], 'a': ['1', '-19/21']}], ['control: lowpass wc=1 fs=1', ['lowpass', '1', '1'], {'b': ['1/3', '1/3'], 'a': ['1', '-1/3']}], ['control: lowpass wc=3 fs=1/2', ['lowpass', '3', '1/2'], {'b': ['3/4', '3/4'], 'a': ['1', '1/2']}], ['control: lowpass wc=2000 fs=48000', ['lowpass', '2000', '48000'], {'b': ['1/49', '1/49'], 'a': ['1', '-47/49']}]], [['regression: highpass wc=2000 fs=48000', ['highpass', '2000', '48000'], {'b': ['48/49', '-48/49'], 'a': ['1', '-47/49']}], ['regression: highpass wc=1/2 fs=2', ['highpass', '1/2', '2'], {'b': ['8/9', '-8/9'], 'a': ['1', '-7/9']}], ['regression: highpass wc=3 fs=1/2', ['highpass', '3', '1/2'], {'b': ['1/4', '-1/4'], 'a': ['1', '1/2']}], ['control: lowpass wc=1/2 fs=2', ['lowpass', '1/2', '2'], {'b': ['1/9', '1/9'], 'a': ['1', '-7/9']}], ['control: bad spec', ['lowpass', '0', '1'], 'bad-spec'], ['control: lowpass wc=100 fs=1000', ['lowpass', '100', '1000'], {'b': ['1/21', '1/21'], 'a': ['1', '-19/21']}], ['control: lowpass wc=1 fs=1', ['lowpass', '1', '1'], {'b': ['1/3', '1/3'], 'a': ['1', '-1/3']}]], [['regression: highpass wc=1 fs=1', ['highpass', '1', '1'], {'b': ['2/3', '-2/3'], 'a': ['1', '-1/3']}], ['regression: highpass wc=3 fs=1/2', ['highpass', '3', '1/2'], {'b': ['1/4', '-1/4'], 'a': ['1', '1/2']}], ['regression: highpass wc=1/2 fs=2', ['highpass', '1/2', '2'], {'b': ['8/9', '-8/9'], 'a': ['1', '-7/9']}], ['control: lowpass wc=3 fs=1/2', ['lowpass', '3', '1/2'], {'b': ['3/4', '3/4'], 'a': ['1', '1/2']}], ['control: lowpass wc=2000 fs=48000', ['lowpass', '2000', '48000'], {'b': ['1/49', '1/49'], 'a': ['1', '-47/49']}], ['control: lowpass wc=1/2 fs=2', ['lowpass', '1/2', '2'], {'b': ['1/9', '1/9'], 'a': ['1', '-7/9']}], ['control: bad spec', ['lowpass', '0', '1'], 'bad-spec']], [['regression: highpass wc=1/2 fs=2', ['highpass', '1/2', '2'], {'b': ['8/9', '-8/9'], 'a': ['1', '-7/9']}], ['regression: highpass wc=100 fs=1000', ['highpass', '100', '1000'], {'b': ['20/21', '-20/21'], 'a': ['1', '-19/21']}], ['regression: highpass wc=1 fs=1', ['highpass', '1', '1'], {'b': ['2/3', '-2/3'], 'a': ['1', '-1/3']}], ['control: lowpass wc=100 fs=1000', ['lowpass', '100', '1000'], {'b': ['1/21', '1/21'], 'a': ['1', '-19/21']}], ['control: lowpass wc=1 fs=1', ['lowpass', '1', '1'], {'b': ['1/3', '1/3'], 'a': ['1', '-1/3']}], ['control: lowpass wc=3 fs=1/2', ['lowpass', '3', '1/2'], {'b': ['3/4', '3/4'], 'a': ['1', '1/2']}], ['control: lowpass wc=2000 fs=48000', ['lowpass', '2000', '48000'], {'b': ['1/49', '1/49'], 'a': ['1', '-47/49']}]], [['regression: highpass wc=3 fs=1/2', ['highpass', '3', '1/2'], {'b': ['1/4', '-1/4'], 'a': ['1', '1/2']}], ['regression: highpass wc=2000 fs=48000', ['highpass', '2000', '48000'], {'b': ['48/49', '-48/49'], 'a': ['1', '-47/49']}], ['regression: highpass wc=1/2 fs=2', ['highpass', '1/2', '2'], {'b': ['8/9', '-8/9'], 'a': ['1', '-7/9']}], ['control: lowpass wc=1/2 fs=2', ['lowpass', '1/2', '2'], {'b': ['1/9', '1/9'], 'a': ['1', '-7/9']}], ['control: bad spec', ['lowpass', '0', '1'], 'bad-spec'], ['control: lowpass wc=100 fs=1000', ['lowpass', '100', '1000'], {'b': ['1/21', '1/21'], 'a': ['1', '-19/21']}], ['control: lowpass wc=1 fs=1', ['lowpass', '1', '1'], {'b': ['1/3', '1/3'], 'a': ['1', '-1/3']}]]]
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: highpass wc=100 fs=1000 | {'a': ['1', '-19/21'], 'b': ['20/21', '-20/21']} | {'a': ['1', '-19/21'], 'b': ['20/21', '-20/21']} | Passed |
| regression: highpass wc=1 fs=1 | {'a': ['1', '-1/3'], 'b': ['2/3', '-2/3']} | {'a': ['1', '-1/3'], 'b': ['2/3', '-2/3']} | Passed |
| regression: highpass wc=3 fs=1/2 | {'a': ['1', '1/2'], 'b': ['1/4', '-1/4']} | {'a': ['1', '1/2'], 'b': ['1/4', '-1/4']} | Passed |
| control: lowpass wc=100 fs=1000 | {'a': ['1', '-19/21'], 'b': ['1/21', '1/21']} | {'a': ['1', '-19/21'], 'b': ['1/21', '1/21']} | Passed |
| control: lowpass wc=1 fs=1 | {'a': ['1', '-1/3'], 'b': ['1/3', '1/3']} | {'a': ['1', '-1/3'], 'b': ['1/3', '1/3']} | Passed |
| control: lowpass wc=3 fs=1/2 | {'a': ['1', '1/2'], 'b': ['3/4', '3/4']} | {'a': ['1', '1/2'], 'b': ['3/4', '3/4']} | Passed |
| control: lowpass wc=2000 fs=48000 | {'a': ['1', '-47/49'], 'b': ['1/49', '1/49']} | {'a': ['1', '-47/49'], 'b': ['1/49', '1/49']} | Passed |
SHA-256 / 87e338a50af053e4afac2dcde72db63058245302caf33ee73693ff074cb2bab0
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 2026-09-29T14:51:38.677478+00:00.
Case digest / 17f4c72699eeb3b2fecf58b65bad9053025a89fc50983f56e561792ad4e2bd42