dual op• 資料種類:signal × signal → table
• 呼叫: import fullseye as fs; fs.ledger.transfer_function(x, y, rate, win=None, hop=None, window='hann', estimator='h1', ref=1.0, floor_db=-200.0)(要直接呼叫實作,import acoustics; acoustics.transfer_function(x, y, rate, win=None, hop=None, window='hann', estimator='h1', ref=1.0, floor_db=-200.0);從台帳取用則 opsacoustics.get("transfer_function"))
以 x 為輸入、y 為輸出估計 H(f),並給出同調。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
estimator:
• "h1" — Pxy / Pxx. Unbiased when the noise is on the output. The usual default and the right one for a driven test.
• "h2" — Pyy / conj(Pxy). Unbiased when the noise is on the input. It over-estimates the magnitude wherever H1 under-estimates it, so the two together bracket the truth, and |H1/H2| = gamma**2 exactly — an identity worth checking rather than a coincidence.
Returns a dict: freqs, response (complex), magnitude, magnitude_db (relative to ref), phase_rad, coherence, estimator, n_frames, win, hop, rate.
Measured at 16 kHz over 16384 samples, win = 1024, 31 frames, white input:
• y = 2.5 * x: mean |H| = 2.5000000000, max deviation from 2.5 over all bins 1.78e-15, mean |phase| 2.7e-17, mean coherence 1.0000000000.
• y = 0.8 * x[n-37]: the phase is a straight line in frequency of slope -2 pi * 37 / 16000 s. A least-squares fit to the unwrapped phase over 200-7000 Hz gives a group delay of 37.000004 samples against a true 37 (error 4.3e-06 samples), and mean |H| = 0.792220 over the same bins against a true 0.8 (max deviation 0.050).
• y = 2.5 * x + n with output noise at 0 dB SNR: H1 gives mean |H| = 2.523390 — 0.94 % from the truth — while H2 gives 5.043020, a factor of 2.0 too large, exactly as the theory predicts when the noise sits on the output. And |H1/H2| equals the coherence pointwise to 5.6e-16 (both mean 0.509143), which is the identity worth
knowing: the ratio of the two estimators *is* the coherence.
That third row is why the coherence is returned with the response. The H2 number is off by 100 % and there is nothing about 5.04 that looks wrong.
Raises ValueError: everything coherence refuses, plus an unknown estimator and ref <= 0.
• 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
• poc_leak_localization — py -3.11 examples/poc_leak_localization.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.