k·fs transmission zeros, the economy preset, the program-weighted metric, and the book's epilogue#31
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…ighted metric The music-dsp thread's suggestion, productionized inside the passband spec. designPrototypeCompensated builds the droop pre-compensation as a cosine series in f (weighted LS via a small dense solver) -- in time, a sum of the brickwall kernel at integer shifts, so the design stays closed-form with no FFT -- then windows and convolves with a one-sample rect whose zeros land on every k*fs. Two direct-DFT correction passes hold ripple to +/-0.003 dB on every preset. The composite is centered at (L*T-1)/2 exactly like the plain design (the even-length rect shifts by half a fine sample; the fractional-delay tests caught the -72 dB error of getting that wrong). balanced/transparent flip to imageZeros (equal taps, worst-case numbers unchanged, low-band folded images 10-20 dB deeper); fast stays plain. New economy preset (L=512, T=32, zeros): 2/3 of balanced's per-sample compute, measured 131.6 dB on the new program-weighted metric vs balanced's 134.5 -- the RBJ trade, quantified -- with the worst-case 19.5 kHz sine at 77 dB kept visible in tests and docs. New tests/support/multitone_analysis.hpp: 24 pink-weighted log-spaced tones, joint LS fit (sequential fit-subtract floors at 48 dB; measured), DC modeled in the fit (subtracting the sample mean beforehand injects a constant the sine basis cannot absorb -- also measured, also 48 dB), Fisher-weighted clock-ratio pooling. An instrument self-test pins the floor at >145 dB on synthetic tones. Fractional-delay and Q15 DC-gain gates re-pinned to the documented +/-0.01 dB passband contract (the old numbers leaned on the plain Kaiser's incidental +/-0.0001 dB flatness); a half-sample alignment bug still fails them by >20 dB. https://claude.ai/code/session_01HuAFfoeD5a5Xe5aGNA16M9
The RBJ episode as the book's closing chapter: verify before you argue (his 108/120/12-per-doubling figures reproduced to half a dB), the T=32 claim refuted at the worst-case spec and then understood as a different spec, the k*fs zeros productionized inside the passband contract (with the half-sample rect-centering bug the fractional-delay tests caught), the program-weighted instrument and its own two measured 48 dB failure modes, and the economy preset's 131.6-vs-134.5 dB outcome. George Box epigraph. Live excerpts via pw_* anchors; the pw_comp_design anchor is re-scoped to the design contract with pw_comp_rect for the zeros themselves. https://claude.ai/code/session_01HuAFfoeD5a5Xe5aGNA16M9
The ratchet's first run priced the naive design loops at +225.4M instructions per M55 scenario (constant across all seven -- pure constructor cost, audio path untouched): ~2M libm sin/cos calls, and far worse where doubles are soft (seconds of boot on an M33-class part). Before ratifying baselines at that price: sin(pi*c*(t-m)) now expands by angle addition over M+1 precomputed shift constants with the per-tap sin/cos advanced by a unit rotator (re-synced via libm every 4096 taps); the probe DFT uses one rotator per frequency; the fit basis uses the Chebyshev recurrence. ~3k libm calls remain. Coefficients move only at rotator-rounding level; all 70 host tests pass unchanged, including the ripple/zero/alignment gates. https://claude.ai/code/session_01HuAFfoeD5a5Xe5aGNA16M9
Trig-lite constructor measured at +33.7M instructions per M55 scenario, constant across all seven (the audio path's counts are unchanged; the delta is construction only), down from the naive form's +225.4M. Justification: PERFORMANCE.md 'Compensated prototype design' entry. README icount table regenerated by scripts/update_icount_docs.py. The ratchet job stops at the first failing target, so m33 and hexagon baselines follow from the next runs' logs (documented bootstrap pattern). Also drops the README's stale private-repo note. https://claude.ai/code/session_01HuAFfoeD5a5Xe5aGNA16M9
…rgets The M33 leg priced the trig-lite design at +1.90G instructions per scenario: on a soft-FP64 target every double flop is a ~140-instruction libcall, so the ~14M design flops -- not libm -- were the bottleneck there. Cut to one correction pass and 24 probes: ripple margin still >=2.2x on every preset (balanced/transparent/economy re-verified, including 16 kHz scaling), roughly halving the design flops. Two passband-edge fractional-delay gates re-pinned between the new measured ripple and the +/-0.01 dB contract bound. Known-debt entry records the remaining constructor cost on soft-FP64 targets, the ratchet-sensitivity dilution, the construction-as-its-own-scenario follow-up, and the RP2350 DCP caveat. CI: the ratchet job's M33/Hexagon steps now run even when an earlier target fails (if: !cancelled()) -- each target's numbers are independent evidence, and stopping at the first failure forced a serial baseline harvest. https://claude.ai/code/session_01HuAFfoeD5a5Xe5aGNA16M9
One run, all targets (the !cancelled() decoupling): M55 +16.1M
(hardware FP64), Hexagon +131.3M, M33 +928.7M (soft-FP64) instructions
of construction per scenario, constant across all seven scenarios per
target -- the constant-delta signature confirming the audio path is
untouched. The M55 leg tripped the two-sided ratchet downward
('IMPROVED beyond tolerance') against the interim two-pass baselines,
which is the gate working as designed. README icount table regenerated.
https://claude.ai/code/session_01HuAFfoeD5a5Xe5aGNA16M9
The baseline-harvest rounds queued six full CI stacks for dead commits, each holding runners through QEMU target builds. Pushes now cancel their own branch's in-flight runs; the latest commit is the only one that matters for every gate in this repository. https://claude.ai/code/session_01HuAFfoeD5a5Xe5aGNA16M9
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What this is
The two experiments from the music-dsp (RBJ) thread, productionized, plus the book chapter that tells the story. Follows from the verification notebook (#30).
The design change
detail::designPrototypeCompensatedplaces transmission zeros at every integer multiple of the sample rate (one-sample-rect convolution) with the sinc droop pre-compensated inside the passband spec: the 1/sinc tilt is expressed as a short cosine series (weighted LS via a small dense solver) — in time, a sum of the brickwall kernel at integer shifts, so the design stays closed-form with no FFT. Two direct-DFT correction passes hold ripple to ±0.003 dB on every preset. The composite is centered exactly like the plain design; the fractional-delay tests caught the half-fine-sample rect-centering bug (−72 dB at 1 kHz, +6 dB/octave) on the first build, as designed.balanced/transparentflip toimageZerosat equal tap count: worst-case numbers unchanged, passband flat to ±0.003 dB, low-band folded images 10–20 dB deeper (997 Hz prototype floor: −144 → −158 dB).faststays plain.economypreset (L=512, T=32, zeros): two-thirds of balanced's per-sample compute, 0.16 ms less group delay.The new metric
tests/support/multitone_analysis.hpp: 24 pink-weighted log-spaced tones, joint LS fit (sequential fit-subtract floors at 48 dB — measured), DC modeled in the fit (pre-subtracting the sample mean also floors at 48 dB — measured; a finite tone window has a legitimate mean), Fisher-weighted clock-ratio pooling.ProgramWeighted.InstrumentFloorpins the instrument itself at >145 dB on synthetic tones (measured 151.9).Measured outcome (full converter, +200 ppm)
RBJ's trade, quantified: 2.9 dB of program-weighted quality for 33% of the compute, with the worst-case number kept visible in docs, tests, and the book.
Test-gate re-pins
Fractional-delay and Q15 DC-gain gates re-pinned to the documented ±0.01 dB passband contract (the old numbers leaned on the plain Kaiser's incidental ±0.0001 dB flatness); alignment bugs still fail them by >20 dB. Host suite: 70/70 under
-Werror.Expected CI note — embedded ratchet
Constructor design cost grew ~3× in transcendentals (still constructor-only, off the audio path; audio-path instruction counts are unchanged — same T, same kernels). Embedded icount scenarios include construction, so the ±3% two-sided ratchet will trip on short scenarios; per the algorithm-change rule I'll regenerate baselines from this PR's CI logs and push them here, with the PERFORMANCE.md entry (included) as justification.
The book
New epilogue chapter, "A letter from the list": the whole episode — verify-before-you-argue, the two-specifications lesson, the instrument's own two measured failure modes — with live
pw_*excerpts from the new code. George Box epigraph.🤖 Generated with Claude Code
https://claude.ai/code/session_01HuAFfoeD5a5Xe5aGNA16M9
Generated by Claude Code