fullseye

coherence — ACOUSTICS dual op

使い方

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 :func:_as_signal refuses on either channel, unequal channel lengths, fewer than 2 frames, win longer than the record, an unknown window.

詳しい使い方ガイド

参考(サンプルデータ・文献)

実行できる例(この op を実際に呼ぶ検証済みサンプル)

型が繋がる次の op(table を入力に取れる)

istft

同カテゴリ(dual)

transfer_function · gcc_delay


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.