Three shipped filter configurations never return to silence — Phaser defaults hold −4 LSB of DC forever

[bdbarnett]

Evidence from the 2026-09-02 fault-planting pass run by the accuracy session on Brad's "break it" challenge (workflow journal wf_88202b87-a89, each agent in its own worktree, audioif verified byte-identical to HEAD afterwards). Filed by Arthur because that session is write-frozen; the measurements are its, quoted, not mine.

Three shipped configurations across two node types never return to silence. Source driven with a 0.09 s tone then digital silence; residual after 100 s of silence:

configuration	residual
audioeffects.Phaser(src), shipped defaults	−4 LSB, exactly constant, never decays
audiofilters.Phaser(frequency=200, stages=2, 48 kHz)	−179 LSB, about −45 dBFS of DC
audiofilters.Phaser(frequency=1000, stages=2, 48 kHz)	−36 LSB
audioeffects.LowPass(src, frequency=100.0), default q	+1 LSB DC, forever
audioeffects.LowPass(src, frequency=40.0, q=8.0)	−4 LSB DC, forever

Cause

The biquad is fixed-point (audioif_biquad.h: int32 coefficients with a per-filter shift, int32 state with 12 fractional bits). At low W0 it settles on a stuck DC value rather than zero.

Why the parity probe sits exactly where the fault is not

audiofilters.Phaser(frequency=1234, sample_rate=8000) — the probe's exact configuration — measures residual 0. It differs from the product on all four axes that decide this: 8 kHz vs 48 kHz, a static 1234 Hz vs an LFO sweeping 470–1730 Hz, 0.256 s vs minutes, and a never-silent random source vs real silence between notes. The probe occupies the one cell of the grid where the property holds.

Why nothing in the suite catches it

Five places assert nodes are not silent (assertGreater(peak, 0.001, "%s renders silence") — test_cpython_effects_library.py:245, test_cpython_instruments.py:75, :85, test_cpython_render.py:175, :685). Exact-zero output is asserted in only two places, test_cpython_dsp_nodes.py:83 (Dynamics) and :163 (Splitter), two blocks each, both stateless passthrough. No recursive node is ever asked to go quiet.

A −4 LSB DC offset held forever on a shipped default is a product defect, not a test nit: it is a DC component in every rest.

[bdbarnett]

Held by Brad 2026-09-03. Fixing the fixed-point biquad's stuck DC changes what three shipped effect configurations sound like, and he wants to hear it before it lands. Stays open as filed with its evidence; not part of the accuracy session's 12-hour goal. Further measurement (which W0 values stick, at what residual) is welcome here; a fix is not, yet.

[bdbarnett]

Measurement only — the fix is held for Brad's ear, and this does not touch the biquad

Asked for "which W0 values stick, at what residual". I could not reproduce a stuck residual under the conditions I could afford to run, and that is not a refutation — my conditions differ from the report's on three axes.

Swept a plain LOW_PASS biquad through audiofilters.Filter at 8 kHz, impulse then silence, residual read after ~1.5 s:

freq (Hz)	W0	settled residual
20	0.0157	0
40	0.0314	0
80	0.0628	0
160	0.1257	0
320	0.2513	0
640	0.5027	0
1280	1.0053	0

How this differs from the reported cases, which is why it settles nothing:

• Sample rate. Reported at 48 kHz; measured at 8 kHz. W0 is the ratio, so the same W0 is reached at a different frequency — but the coefficient rounding that produces a stuck value depends on the coefficients, not on W0 alone.
• Node. Reported for audioeffects.Phaser, audiofilters.Phaser and audioeffects.LowPass. Measured on a bare LOW_PASS biquad. The Phaser is an all-pass cascade with its own feedback path; audioeffects.LowPass wraps the filter with defaults I did not replicate.
• Duration. Reported "after 100 s of silence". Measured over ~1.5 s. A residual that decays very slowly rather than sticking would read as zero here.

Two attempts at the reported configuration directly (48 kHz, 6 s and then 0.5 s of silence through audioeffects.Phaser) exceeded a 2-minute budget and were killed — pure-Python effect rendering is roughly real-time, so 100 s of silence is 100 s of compute per configuration, times several configurations.

What would settle it cheaply: read the settled state out of the biquad directly rather than rendering audio through it — audioif_biquad.h keeps int32 state with 12 fractional bits, so the stuck value is visible in the state variables without waiting for it in the output. That is the measurement worth doing before anyone changes the coefficients, and it is minutes rather than hours.

Recorded so the next person does not repeat the slow path. No biquad change made — the fix alters what three shipped effects sound like and is held for Brad.

[bdbarnett]

Phase 0 of the effects program — the 48 kHz settled-state measurement this issue's second comment asked for.

Posted from audiocomponents/docs/effects-survey.md §"audioif#23 — the settled DC residual, verbatim", verbatim. Measured 2026-09-06/07 on the CPython build of audioif in audiocomponents/.venv. The effects roadmap's Gate 0 required this table "either way"; this is it.

The roadmap's Gate 0 requires the 48 kHz settled-state measurement for every shipped EQ and Phaser configuration, with the result posted to audioif#23 either way. The table below is the measurement as recorded. all_reach_zero is FALSE — three configurations hold a permanent non-zero constant — so the DC-clean candidate is not refuted, and candidate 9 stands.

audioif#23 — settled DC residual of the shipped fixed-point biquad. 48 kHz stereo, 0.09 s of 1 kHz at −6 dBFS (peak 16422) then digital silence, pulled to 600 blocks. "Settled residual" is the peak |sample| of the final block; every non-zero residual below is a single constant value across all frames of the block (true DC, not ringing). "Blocks to settle" counts output blocks after the first all-silent input block until the output block stops changing for good.

Configuration	W0 (rad/sample)	Settled residual (LSB)	Blocks to settle
LowPass, defaults (1000 Hz, q=0.707)	0.130900	0	0
HighPass, defaults (1000 Hz, q=0.707)	0.130900	0	0
BandPass, defaults (1000 Hz, q=0.707)	0.130900	0	0
Notch, defaults (1000 Hz, q=0.707)	0.130900	0	0
ParametricEQ, defaults bands=() — builds no biquad, _output = source	n/a	0	0
ParametricEQ, one bell 1000 Hz +6 dB q=1.4 (added: the default is a wire)	0.130900	0	1
GraphicEQ, defaults (flat ⇒ every band dropped, no biquad)	n/a	0	0
GraphicEQ, +6 dB on the 1 kHz band, q=1.4 (added: the default is a wire)	0.130900	0	1
DynamicEQ, defaults (3000 Hz, q=2.0; notch + band-pass) †	0.392699	0	1
Phaser, defaults (6 all-pass stages) ‡	0.143990	4 (constant −4)	20
LowPass, 100 Hz, default q=0.707	0.013090	1 (constant +1)	2
LowPass, 40 Hz, q=8	0.005236	4 (constant −4)	33

† DynamicEQ's output is its audiomixer.Mixer, which hands out 128-frame blocks; every other row is 512 frames per block. Its "1 block" is therefore ~2.7 ms, not ~10.7 ms.

‡ The Phaser does not use the shipped biquad. grep -rln audioif_biquad /home/brad/gh/pydevices/audioif/src/ matches only synthio/Biquad.{c,h}, shared/audioif_biquad.{c,h}, shared/audioif_trig.h and cpython/_audioif.c — not shared/audioif_phaser.c. Its hold comes from its own int16_t allpass_words[] / feedback_words[] (audioif_phaser.c:28-38), which are in plain sample units with no fractional bits. Listed because the brief asked for it; it is a separate defect from #23, in a CircuitPython-ported node.

Endurance. The three non-zero residuals are permanent, not slow decays: re-run to 3000 blocks (32 s of audio) with the settle window excluded, the set of distinct sample values over blocks 60..3000 is exactly [1] for LowPass 100 Hz, [-4] for LowPass 40 Hz q=8, and [-4] for the Phaser. Block 100 and block 2999 are identical.

Why a residual sticks (from /home/brad/gh/pydevices/audioif/src/shared/audioif_biquad.h and .c, line numbers by grep -n). The header defines AUDIOIF_BIQUAD_STATE_SHIFT 12 (audioif_biquad.h:14) and states that audioif_biquad_state_t.y[2] "carries AUDIOIF_BIQUAD_STATE_SHIFT extra fractional bits" while x[2] is in sample units (audioif_biquad.h:22-26). In audioif_biquad_process (audioif_biquad.c:159-182) the feedback recursion runs entirely in that 12-extra-bit domain: with the input and both x history taps at zero, accumulator = -(a1*y0 + a2*y1), output = (accumulator + rounding) >> shift (line 173), and the sample the caller sees is (output + 2048) >> 12 (lines 177-178). Two consequences: (a) the recursion is round-to-nearest at every step, so once the per-sample change in y falls below half a quantum the state reproduces itself exactly and stops moving — there is no dither and no leak term to drag it to zero; (b) because the state has 12 bits below the sample LSB, a parked y of magnitude ≥ 2048 still rounds up to a visible ±1 or more at the output. The lower W0 is, the closer a1 → -2·2^shift, a2 → +2^shift and the sooner the increment falls under a quantum — which is exactly the ordering measured: 0 LSB at W0 = 0.1309, 1 LSB at W0 = 0.01309, 4 LSB at W0 = 0.005236 with q=8 (high Q also lengthens the approach, 33 blocks vs 2).

Harness note that mattered. audiocore.RawSample._get_buffer returns the whole buffer in one call (32880 frames here), and audioroute.Splitter._pull writes that straight into an 8192-frame ring whose write drags every lagging tap cursor forward (audioif_splitter.c:33-38). Feeding DynamicEQ a plain RawSample therefore laps the ring and reads only the silent tail — output is all zeros and the measurement is void. The final probe replaces RawSample with a 512-frame-per-pull block source, which is why every row above shows a non-zero tone peak (11618…28521) before the silence.

Reading it

Three findings the seeds and the Gate 0 answer must carry:

1. The candidate is not refuted. The refutation condition the roadmap sets — "refuted only if every configuration reaches exact zero" — is not met: three configurations hold a permanent constant, verified to 32 s of audio.
2. Two of the twelve rows are wires, not measurements. ParametricEQ at bands=() and GraphicEQ flat build no biquad at all, so their zeros say nothing; the probe added one bell each so the table measures the biquad rather than the default. This is the absence-reads-as-agreement shape, caught inside the measurement.
3. The Phaser row is a different defect in a different, ported kernel. It is listed because Gate 0 asked for it, but audioif_phaser.c does not call audioif_biquad at all — its hold comes from its own int16 allpass_words[], which is why candidate 9 must carry an all-pass kernel beside the biquad, and why the Phaser's row cannot be fixed by fixing Three shipped filter configurations never return to silence — Phaser defaults hold −4 LSB of DC forever #23.
4. Every future number must name its rate and channel count. The refuter's independent re-measurement found the Phaser hold at 48 kHz stereo and exact zero at 22.05 kHz mono on the identical probe. A run at another rate will read clean and look like the defect is gone.

---

One thing this table does not settle, and it should not sit inside this issue.

The Phaser row is a separate defect in a different kernel, and it is a CircuitPython-ported one. audioif_phaser.c never calls audioif_biquad — grep -rln audioif_biquad src/ matches only synthio/Biquad.{c,h}, shared/audioif_biquad.{c,h}, shared/audioif_trig.h and cpython/_audioif.c. The Phaser's hold comes from its own int16_t allpass_words[] / feedback_words[] (audioif_phaser.c:28-38), in plain sample units with no fractional bits. Fixing #23's fixed-point biquad will therefore not move the Phaser's −4 LSB by one bit, and this issue's title carries the Phaser as though it would.

It is filed as its own audioif issue rather than left here. This issue stays what its cause paragraph says it is: the AUDIOIF_BIQUAD_STATE_SHIFT 12 recursion in audioif_biquad.c:159-182.

[bdbarnett]

Re-measured today. The three shipped configurations this issue is titled for now return to exact silence. What remains is the upstream half, which is a held report.

Fixed: our own classes

Same method as the original — 0.09 s of 220 Hz, then digital silence — sampled at 1, 5, 15, 30 and 59 seconds into the silence:

configuration	was	now
audioeffects.Phaser(src), shipped defaults	−4 LSB, constant, never decays	0 at every checkpoint
audioeffects.LowPass(src, frequency=100.0)	+1 LSB DC forever	0
audioeffects.LowPass(src, frequency=40.0, q=8.0)	−4 LSB DC forever	0

The cause of the fix is a node change, not a kernel one: both classes now declare REQUIRES = ("audiobiquad", ...) and build their sections from audiobiquad.Biquad rather than the fixed-point path. audiobiquad has float state and flushes anything below 1e-20, so a tail arrives at zero instead of parking near it — that is trait B4 in tests/test_cpython_audiobiquad.py, "every mode's tail reaches exact zero and stays there".

So the product defect is gone: no DC component in a rest, on either shipped class.

Not fixed, and not ours: audiofilters.Phaser

The other two rows are CircuitPython's node, and they are unchanged. Measured today with the same source:

audiofilters.Phaser  200 Hz stages=2  ->  residual -179
audiofilters.Phaser 1000 Hz stages=2  ->  residual  -36

Identical to the figures filed here. That is audioif#36's subject — the Phaser's own int16 all-pass state, distinct from the biquad — and it is one of the three upstream reports being held until we have done a good deal more work across the org (Brad, 2026-09-09). Nothing to submit today.

The test gap this issue named is worth keeping open a moment longer

The original filing made a sharper point than the residuals: five places in the suite assert nodes are not silent, exact-zero output was asserted in only two, and no recursive node was ever asked to go quiet. That is why a −4 LSB rest shipped.

That gap is now partly closed — audiobiquad's B4 asks exactly that, across every mode, and test_cpython_silenced_voice.py added today asks it of a synthio voice — but it is closed for the nodes someone thought to cover, not by construction. Worth a look during the effects work at whether every recursive node in the shipped library has a tail-reaches-zero assertion, rather than assuming the two that have one are representative.

Left open on purpose

Closing this would lose the audiofilters.Phaser rows, which are the evidence behind #36 and behind the held report. Suggest it stays open, retitled around the upstream half, and closes with #36 when that report is filed and accepted — or sooner if you would rather track only #36 and close this now that the product half is fixed.

[bdbarnett]

Closing per Brad: the product half is fixed (measured above — all three shipped configurations return to exact zero), and the remaining audiofilters.Phaser rows are tracked by audioif#36, which carries the held upstream report. Tracking one issue rather than two.