dual op• データ種: signal × signal → table
• 呼び出し: import fullseye as fs; fs.ledger.coherence(x, y, rate, win=None, hop=None, window='hann') (実装を直接呼ぶなら import acoustics; acoustics.coherence(x, y, rate, win=None, hop=None, window='hann')、台帳から引くなら opsacoustics.get("coherence"))
Ordinary coherence: how much of y is linearly explained by x.
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 _as_signal refuses on either channel, unequal channel lengths, fewer than 2 frames, win longer than the record, an unknown window.
• 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
table を入力に取れる)dual)*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.