level op• 資料種類:signal → signal
• 呼叫: import fullseye as fs; fs.ledger.apply_weighting(x, rate, kind='A')(要直接呼叫實作,import acoustics; acoustics.apply_weighting(x, rate, kind='A');從台帳取用則 opsacoustics.get("apply_weighting"))
對訊號施加 A / C / Z 頻率加權,零相位。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
The weighting is applied as a real, even gain in the frequency domain, so it introduces no phase distortion and no group delay — the result is aligned sample-for-sample with the input, which a recursive filter implementation would not be.
Measured: a 1 kHz sine at 16 kHz (16000 samples, exactly 1000 periods) is returned unchanged by both A and C weighting — max absolute difference 1.078e-13 for A and 1.225e-13 for C — because both curves are exactly 0 dB at 1 kHz by construction. A 100 Hz sine of amplitude 1.0 comes back with amplitude 0.110373 under A weighting, against the closed form 10**(-19.1428/20) = 0.110373.
kind="Z" returns a copy, unchanged.
A tone that is not a whole number of periods in the record reads too loud, by up to 17 dB, and nothing raises. The multiplication is over the record's own DFT, which treats it as periodic; a tone that does not close on itself leaks across every bin. That leakage would be harmless if the weighting were flat, but A weighting spans about 40 dB between 20 Hz and 1 kHz, so a sidelobe 40 dB below a 31.5 Hz tone arrives at 1 kHz weighted 40 dB *higher* and takes over the sum. Measured, 0.5 s at 48 kHz, error against the closed-form A(f) for a pure tone:
========== ============= ========== ==============
f (Hz) periods error (dB) bin-centred?
========== ============= ========== ==============
22.0 11.0 +0.0000 yes
31.5 15.75 +7.7986 no
20.5 10.25 +17.2116 no (worst, 20-200 Hz)
63.0 31.5 +0.1121 no
100.0 50.0 +0.0000 yes
1000.0 500.0 -0.0000 yes
========== ============= ========== ==============
31.5 Hz is a nominal one-third-octave centre, so this is a path a real measurement walks into rather than a contrived one. The error is always *positive* — leakage only ever adds power at frequencies the curve favours.
Two things confirm the diagnosis is dynamic range and not arithmetic. The same 31.5 Hz tone under C weighting, whose tilt over the same span is a few dB rather than forty, is off by only +0.0493 dB. And lengthening the record to where the tone *does* close on itself removes it entirely: at 31.5 Hz the error is +7.7524 dB over 0.25 s, +7.7986 over 0.5 s, +0.4615 over 1 s, and -0.0000 over 2 s and 4 s (63 and 126 whole periods).
Two candidate cures were measured (error in dB against the closed form, 0.5 s at 48 kHz):
=================================== ======== ======== ========
treatment 31.5 Hz 20.5 Hz 22.0 Hz
=================================== ======== ======== ========
as implemented (rectangular) +7.7986 +17.2116 +0.0000
zero-pad x4 (linear convolution) +5.5620 +14.3352 +0.7969
Hann window, corrected for its gain +0.0534 +0.1841 +0.1505 =================================== ======== ======== ========
Padding barely helps — zero-padding a tone puts an abrupt edge into the record and an edge is broadband. A Hann window does essentially cure it, turning +17 dB into +0.18 dB, at the cost of the bin-centred columns which go from exactly 0 to about 0.15 dB. So why is it not the default?
Because it would trade a loud error for a quiet one. L_eq is an *energy average over the record*, and a window is not energy-preserving for anything that is not stationary. Measured with Z weighting (so the window is the only thing acting) on a 50 ms 1 kHz burst inside a 0.5 s record, all three placements being -13.0103 dB unwindowed as they must be:
============== ============ ===========
burst position Hann (dB) difference
============== ============ ===========
start -36.0587 -23.05
centre -8.8218 +4.19
end -36.0587 -23.05
============== ============ ===========
A window makes the answer depend on *where in the record the sound happened*, which is precisely the "plausible wrong number" this module refuses to ship by default. So the rectangular behaviour stays, and the Hann estimate is available by asking for it: equivalent_level(..., window="hann"). Use it when the record is stationary and tonal — which is exactly when the leakage bites — and never when the level of a transient is the point.
A cure with neither cost is a different implementation entirely: the standard cascade of A-weighting biquads in the time domain, which would give up the exact-0-dB-at-1-kHz-by-construction property this function is built on, and the zero group delay promised above.
Also worth doing: give the analysis enough record that the content is many periods long, prefer durations that are whole multiples of the period you care about, and read a low-frequency A-weighted level from octave_spectrum (which reports per-band power, so leakage is visible as energy in bands where none belongs) rather than from a single number.
Raises ValueError: everything _as_signal refuses, an unknown kind, rate <= 0.
• acoustic_condition_monitoring 族使用指南
• 範例資料目錄(下載 URL / 授權) —— 2-D 用 skimage.data(BSD/公有領域)加合成圖,3-D 給出真實資料源(Stanford/PDS 等)的下載 URL。
• 運算子來歷與參考文獻 —— 該運算子族所依據的研究/方法出處。
• 演算法的正典(作者、年份)與用途見上面的族使用指南。
• acoustic_condition_monitoring — py -3.11 examples/acoustic_condition_monitoring.py
signal 作為輸入)stft · envelope_spectrum · spectral_kurtosis · cepstrum · angular_resample · order_spectrum · octave_spectrum · weighting_response
level)octave_bands · octave_spectrum · weighting_response · equivalent_level · percentile_level
*Provenance: acoustics.py — ACOUSTICS 運算子登記表。本條目由 tools/opdocs.py md 自動產生(請勿手動編輯)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.