bearing op• データ種: signal → table
• 呼び出し: import fullseye as fs; fs.ledger.cepstrum(x, rate, mode='real', floor_ratio=1e-12, min_quefrency=0.0) (実装を直接呼ぶなら import acoustics; acoustics.cepstrum(x, rate, mode='real', floor_ratio=1e-12, min_quefrency=0.0)、台帳から引くなら opsacoustics.get("cepstrum"))
対数スペクトルのスペクトル —— 周波数軸上の周期構造を見る。
> 以下の詳細説明は原文のままです —— 要約と見出しは訳出済み。
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 _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 ファミリ ガイド
• サンプルデータ カタログ(DL URL / ライセンス) — 2-D は skimage.data(BSD/public)+ 合成、3-D は実データ源(Stanford/PDS 等)の DL URL。
• 演算子の来歴・参考文献 — この op 族の元になった研究/手法の出典。
• アルゴリズムの正典(著者・年)と用途は上記ファミリ使い方ガイドに記載。
• acoustic_condition_monitoring — py -3.11 examples/acoustic_condition_monitoring.py
• poc_web_roll_periodicity — py -3.11 examples/poc_web_roll_periodicity.py
table を入力に取れる)bearing)envelope_spectrum · bearing_defect_frequencies · spectral_kurtosis
*Provenance: acoustics.py — ACOUSTICS operator registry. この per-op ノートは tools/opdocs.py md が自動生成(手編集しない)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.