bearing op• 資料種類:signal → table
• 呼叫:import acoustics; acoustics.cepstrum(x, rate, mode='real', floor_ratio=1e-12, min_quefrency=0.0)(或 opsacoustics.get("cepstrum"))
對數譜的譜 —— 看頻率軸上的週期結構。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
A harmonic family or a family of modulation sidebands is periodic along the
frequency axis, so it collapses to a single line along the cepstrum's
quefrency axis (in seconds). Two things this finds that a spectrum does not:
an echo at delay `tau (a rahmonic at q = tau`) and a **sideband
family** spaced `df apart (a rahmonic at q = 1/df`). The second is the
bearing case — sidebands around a gear mesh spaced at the shaft rate.
`mode`:
• `"real" — irfft(log|X|)`, the standard real cepstrum. Discards phase,
so it cannot be inverted; nothing here pretends otherwise.
• `"power" — irfft(log|X|**2) = 2 * real`, kept because the two
conventions differ by exactly a factor of two and mixing them silently
halves or doubles every amplitude a caller compares against a reference.
`log(0) is handled by flooring the magnitude at floor_ratio` times its
own maximum (default 1e-12, i.e. -240 dB) rather than letting `-inf` enter
the inverse transform, where it would make the entire cepstrum NaN. The
number of floored bins is returned as `floored_bins` — a large count means
the signal is band-limited and the cepstrum is dominated by the flooring, not
by the signal.
`min_quefrency` (seconds) excludes the low-quefrency region from the peak
search. This is not cosmetic. The first few bins carry the **spectral
envelope** — the overall shape of the spectrum, which is large and has
nothing to do with periodic structure — and they dominate. Measured on an AM
tone with sidebands 50 Hz apart, the five largest cepstral values sit at
0.000125, 0.00025, 0.000375, 0.000625 and 0.001 s, i.e. all of them are the
envelope, and the default peak search returns 0.000125 s rather than the
1/50 = 0.02 s a reader would expect. Excluding the envelope is the standard
practice ("liftering") and is the caller's decision, so it is an argument
with a visible default of 0.
Returns a dict: `quefrency (s), cepstrum, rate, mode`,
`floored_bins, min_quefrency, peak_quefrency, peak_amplitude`,
`peak_rate_hz (1/peak_quefrency` — the sideband spacing or repetition
rate the rahmonic corresponds to). The peak is taken over
`min_quefrency < q < n/(2*rate)`; the cepstrum is symmetric past that.
Measured ground truths:
• Echo. White noise at 8 kHz plus 0.6 times itself delayed by 200
samples: `peak_quefrency = 0.025000` s, peak index exactly 200, and
`floored_bins = 0`.
• A periodic family of lines. A 50 Hz impulse train convolved with a
random 64-tap FIR (so the spectrum is broadband with lines every 50 Hz):
peak at `0.020000` s = 50.00 Hz exactly, with
`min_quefrency=0.002`.
• What it looks like when the fundamental is not the largest. The
`mode="impulse"` bearing signal repeats every 1/107 s, and the largest
rahmonic above 2 ms is at 0.037383 s — which is `4/107`, the *fourth*
rahmonic, not the first. A cepstrum reports a family, and reading only
its maximum gives an answer that is off by an exact integer factor and
looks entirely reasonable.
• Where it stops working. An AM tone has three spectral lines and
nothing else; every other bin is floored, the log spectrum is mostly the
floor, and there is no 1/50 s rahmonic to find at all. Cepstral sideband
analysis needs a *broadband* signal — a gear mesh, not a tone.
`mode="power" is exactly twice mode="real"` (measured max difference
0.000e+00).
Raises `ValueError: everything :func:_as_signal` refuses, an unknown
`mode, floor_ratio outside (0, 1), a negative min_quefrency`, a
`min_quefrency` at or past the half-length of the record (nothing would be
left to search), an identically zero signal, and a signal shorter than 4
samples.
• 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
table 作為輸入)bearing)envelope_spectrum · bearing_defect_frequencies · spectral_kurtosis
*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.