Universal Short-Time Fourier Transform: Data-Adaptive Window-Length Selection for Time-Frequency Analysis

Abstract

The short-time Fourier transform (STFT) characterizes the local frequency content of time-varying signals by evaluating the discrete Fourier transform over a sliding analysis window. The STFT is governed by a fundamental resolution trade-off: a short window localizes rapid transients in time at the cost of frequency resolution, whereas a long window resolves closely spaced harmonics at the expense of temporal resolution. The Universal Short-Time Fourier Transform (U-STFT) resolves this trade-off sequentially by modeling the analysis window duration as a data-adaptive state variable that indexes the number of hops included in the current observation interval. At each frame, a bank of candidate window durations is scored using normalized order-three Rényi entropy to quantify joint time-frequency concentration. A window length trellis aggregates the resulting 𝒪(3^M) candidate window schedules with linear complexity per frame, guaranteeing a cumulative mix-loss regret bound of 𝒪((k+1)log M) relative to any hindsight window schedule with k resolution changes over M frames. By linearity of the Fourier transform, posterior expectation across the candidate bank yields a single spectrum equivalent to an STFT evaluated with a data-adaptive effective window, while an envelope-normalized synthesis stream guarantees exact overlap-add reconstruction. Evaluations on synthetic and marine bioacoustic signals demonstrate adaptive resolution tracking, enhanced spectral concentration, and exact time-domain invertibility.

A Localized Core-Tail Fourier-Laguerre Frame Method with Adaptive Frequency Detection for Unbounded-Domain Problems
Chenyang Wang, Zhenyu Zhao, Tinggang Zhao
arXiv13 Sep 2026PreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
The quantum connection, Fourier-Laplace transform, and families of A_∞-categories
Daniel Pomerleano, Paul Seidel
Inventiones mathematicae7 Jul 2026Peer-reviewedLicence not statedFull text17 citedGeometry & topologyOpenAlex
FASS: Discrete Fourier Transform Adapters for Speech Separation With Incremental Learning
Ziye Yang, Xiang Song, Min Zhao +3
IEEE Transactions on Audio, Speech and Language Processing25 Sep 2026Peer-reviewedPublisher termsFull textStatisticsHAL
A comparison of artificial neural networks and partial least squares modelling for the rapid detection of the microbial spoilage of beef fillets based on Fourier transform infrared spectral fingerprints
Efstathios Panagou, Fady Mohareb, Anthoula Argyri +2
Food Microbiology9 Oct 2026Peer-reviewedLicence not statedFull text76 citedGeneral biology StatisticsHAL
The Taylor Integral and a Generalization of the Discrete Fourier Transform
Athanasios Christou Micheas
arXiv30 Aug 2026PreprintarXiv licenceFull textGeneral mathematicsarXiv

Cite

BibTeX RIS

BibTeX

@misc{mittal2026universal,
  title = {{Universal Short-Time Fourier Transform: Data-Adaptive Window-Length Selection for Time-Frequency Analysis}},
  author = {Manan Mittal and Kanad Sarkar and Ryan M. Corey and John R. Buck and Andrew C. Singer},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.37795},
  eprint = {2610.37795},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.37795},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Universal Short-Time Fourier Transform: Data-Adaptive Window-Length Selection for Time-Frequency Analysis
AU  - Manan Mittal
AU  - Kanad Sarkar
AU  - Ryan M. Corey
AU  - John R. Buck
AU  - Andrew C. Singer
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.37795
UR  - https://arxiv.org/abs/2610.37795
AB  - The short-time Fourier transform (STFT) characterizes the local frequency content of time-varying signals by evaluating the discrete Fourier transform over a sliding analysis window. The STFT is governed by a fundamental resolution trade-off: a short window localizes rapid transients in time at the cost of frequency resolution, whereas a long window resolves closely spaced harmonics at the expense of temporal resolution. The Universal Short-Time Fourier Transform (U-STFT) resolves this trade-off sequentially by modeling the analysis window duration as a data-adaptive state variable that indexes the number of hops included in the current observation interval. At each frame, a bank of candidate window durations is scored using normalized order-three Rényi entropy to quantify joint time-frequency concentration. A window length trellis aggregates the resulting 𝒪(3^M) candidate window schedules with linear complexity per frame, guaranteeing a cumulative mix-loss regret bound of 𝒪((k+1)log M) relative to any hindsight window schedule with k resolution changes over M frames. By linearity of the Fourier transform, posterior expectation across the candidate bank yields a single spectrum equivalent to an STFT evaluated with a data-adaptive effective window, while an envelope-normalized synthesis stream guarantees exact overlap-add reconstruction. Evaluations on synthetic and marine bioacoustic signals demonstrate adaptive resolution tracking, enhanced spectral concentration, and exact time-domain invertibility.
ER  -

Abstract

Related

Cite