transform op• Datenarten: table → signal
• Aufruf: import fullseye as fs; fs.ledger.istft(transform) (die Implementierung direkt: import acoustics; acoustics.istft(transform); aus dem Register: opsacoustics.get("istft"))
Invertiert stft durch gewichtetes Overlap-Add — exakt.
> Die ausführliche Beschreibung unten ist der Originaltext — Zusammenfassung und Überschriften sind übersetzt.
Weighted overlap-add divides the synthesised sum by the overlap sum of the *squared* window, which makes the reconstruction exact for any window and hop satisfying NOLA, not only for the COLA pairs. stft refuses the NOLA violation up front, so if the transform was produced by it the inverse cannot be lossy.
Measured round-trip error, max |x - istft(stft(x))| on 4096 samples of white noise (float64, so 2.2e-16 is one ulp of the largest sample):
=============== ==== ==== ========= =========
window win hop max error nola_min
=============== ==== ==== ========= =========
hann 256 128 1.33e-15 0.5
hann 256 64 1.33e-15 1.5
hann 256 255 2.73e-12 2.27e-08
hamming 256 128 1.33e-15 0.5832
blackman 512 128 1.33e-15 1.206
flattop 256 64 1.33e-15 0.396
boxcar 256 128 8.88e-16 2.0
hann (nfft 512) 256 128 1.33e-15 0.5
=============== ==== ==== ========= =========
Read the third row's two columns together. hop = 255 on a 256-sample window overlaps by one sample, which breaks plain (unweighted) overlap-add completely; weighted overlap-add still inverts it, but only to 2.7e-12 rather than 1.3e-15, because the squared-window overlap sum falls to 2.3e-08 and the reconstruction divides by it. NOLA is satisfied and the result is four orders of magnitude less accurate than every other row — which is why nola_min is *returned* and not merely checked. A NOLA minimum that is small but positive is a conditioning warning, and there is no threshold at which it stops being one, so no threshold is invented here.
Raises ValueError: a dict missing any key stft writes, a spectra whose shape disagrees with the recorded nfft / frame count, or a non-complex spectra.
• Leitfaden zur Familie acoustic_condition_monitoring
• Katalog der Beispieldaten (Download-URLs / Lizenzen) — 2-D nutzt skimage.data (BSD/Public Domain) plus synthetische Bilder, 3-D nennt Download-URLs echter Datenquellen (Stanford, PDS, …).
• Herkunft und Literatur der Operatoren — die Quellen der Forschung/Verfahren, auf denen diese Operatorfamilie beruht.
• Der kanonische Algorithmus (Autor, Jahr) und seine Anwendungen stehen im Familienleitfaden oben.
• acoustic_condition_monitoring — py -3.11 examples/acoustic_condition_monitoring.py
signal als Eingabe)stft · envelope_spectrum · spectral_kurtosis · cepstrum · angular_resample · order_spectrum · octave_spectrum · weighting_response
transform)*Provenance: acoustics.py — ACOUSTICS Operator-Registry. Diese Notiz wird von tools/opdocs.py md erzeugt (nicht von Hand bearbeiten).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.