dual op• Data kinds: signal × signal → table
• Call: import acoustics; acoustics.transfer_function(x, y, rate, win=None, hop=None, window='hann', estimator='h1', ref=1.0, floor_db=-200.0) (or opsacoustics.get("transfer_function"))
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`.
• acoustic_condition_monitoring family guide
• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).
• Operator provenance and references — the sources of the research/methods this op family came from.
• The canonical algorithm (author, year) and its uses are named in the family usage guide above.
• acoustic_condition_monitoring — py -3.11 examples/acoustic_condition_monitoring.py
table as input)dual)*Provenance: acoustics.py — ACOUSTICS operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.