fullseye

transfer_function — ACOUSTICS dual op

• データ種: signal × signal → table
• 呼び出し: 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) (実装を直接呼ぶなら import acoustics; acoustics.transfer_function(x, y, rate, win=None, hop=None, window='hann', estimator='h1', ref=1.0, floor_db=-200.0)、台帳から引くなら opsacoustics.get("transfer_function"))

使い方

Estimate H(f) with x in and y out, with its coherence.

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 :func:coherence refuses, plus an unknown estimator and ref <= 0.

詳しい使い方ガイド

• acoustic_condition_monitoring ファミリ ガイド

参考(サンプルデータ・文献)

• 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。

実行できる例(この op を実際に呼ぶ検証済みサンプル)

• acoustic_condition_monitoring — py -3.11 examples/acoustic_condition_monitoring.py
• poc_leak_localization — py -3.11 examples/poc_leak_localization.py

型が繋がる次の op(table を入力に取れる)

istft

同カテゴリ(dual)

coherence · 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.

This site is open source. Improve this page.