dual op• 資料種類:signal × signal → table
• 呼叫:import acoustics; acoustics.coherence(x, y, rate, win=None, hop=None, window='hann')(或 opsacoustics.get("coherence"))
普通同調:`y 中能被 x` 線性解釋的比例。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
`gamma**2(f) = |Pxy|**2 / (Pxx * Pyy)`, Welch-averaged. It is bounded in
`[0, 1]`, and it is the number that says whether a transfer function is
worth reading at a given frequency.
A single frame makes it identically 1.0 — the Cauchy-Schwarz inequality
is an equality without averaging — so an unaveraged coherence is a perfect
score that carries no information at all. That case is refused, not returned.
`win` defaults to the largest power of two leaving at least 8 frames,
capped at 1024; the value used is returned.
Returns a dict: `freqs, coherence, n_frames, win, hop`,
`rate, mean_coherence, bias` (the coherence a *pair of independent
noise records* would show with this many frames, `1/n_frames` — anything
at or below this is indistinguishable from nothing).
Measured at 16 kHz over 16384 samples, win = 1024, 31 frames:
======================================= ============== ========
case mean coherence min
======================================= ============== ========
y = 2.5 * x (noiseless) 1.000000 1.0000
y = 0.8 * x delayed 37 samples 0.983003 0.9661
y = 2.5 x + independent noise, 0 dB SNR 0.509143 0.2219
y, x independent noise 0.035640 0.0001
======================================= ============== ========
Row three against its closed form: for output noise the expected coherence
is `SNR/(1+SNR)` = 0.5000 at 0 dB, measured 0.5091. Row four against the
bias floor `1/n_frames = 1/31 = 0.0323`, measured 0.0356 — which is why
`bias` is returned: an uncorrelated pair does not read zero, and
reading 0.03 as "a little bit of coupling" is the mistake this number
prevents. Row two shows the other honest limit: a pure delay is a perfectly
linear system and still reads 0.983, not 1, because a delay of 37 samples
moves signal across the frame boundaries the estimator averages over.
Raises `ValueError: everything :func:_as_signal` refuses on either
channel, unequal channel lengths, fewer than 2 frames, `win` longer than
the record, an unknown window.
• 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)dual)*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.