bearing op• 数据种类:signal → table
• 调用:import acoustics; acoustics.cepstrum(x, rate, mode='real', floor_ratio=1e-12, min_quefrency=0.0)(或 opsacoustics.get("cepstrum"))
对数谱的谱 —— 看频率轴上的周期结构。
> 以下的详细说明为原文 —— 摘要与标题已翻译。
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
• 示例数据目录(下载 URL / 许可证) —— 2-D 用 skimage.data(BSD/公有领域)加合成图,3-D 给出真实数据源(Stanford/PDS 等)的下载 URL。
• 算子来历与参考文献 —— 该算子族所依据的研究/方法出处。
• 算法的正典(作者・年份)与用途见上面的族使用指南。
• acoustic_condition_monitoring — py -3.11 examples/acoustic_condition_monitoring.py
table 作为输入)bearing)envelope_spectrum · bearing_defect_frequencies · spectral_kurtosis
*Provenance: acoustics.py — ACOUSTICS 算子登记表。本条目由 tools/opdocs.py md 自动生成(请勿手工编辑)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.