dual op• Data kinds: signal × signal → table
• Call: 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) (to call the implementation directly, import acoustics; acoustics.transfer_function(x, y, rate, win=None, hop=None, window='hann', estimator='h1', ref=1.0, floor_db=-200.0); from the registry, 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 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
• poc_leak_localization — py -3.11 examples/poc_leak_localization.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.