Adaptive window selection improves short-time Fourier transform analysis
Universal Short-Time Fourier Transform: Data-Adaptive Window-Length Selection for Time-Frequency Analysis
Information TheorySound
Summary
Signals like music or animal sounds change over time, and we want to see both the timing and the pitch clearly. The usual way to do this, the short-time Fourier transform (STFT), uses a fixed window size that either captures quick changes well or pitch details well, but not both. The authors created the universal STFT (U-STFT), which picks the best window size as the sound changes, using math to decide on the fly. This leads to clearer time and pitch information while still letting you perfectly rebuild the original sound.
What this means in practice
- •For audio signal engineers: Improve sound analysis tools by automatically adjusting time-frequency resolution to better track complex audio features.
- •For marine bioacoustics analysts: Detect and analyze marine animal sounds more clearly by adaptively tuning signal processing windows over recordings.
Authors
Manan Mittal, Kanad Sarkar, Ryan M. Corey, John R. Buck, Andrew C. Singer
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 $\mathcal{O}(3^M)$ candidate window schedules with linear complexity per frame, guaranteeing a cumulative mix-loss regret bound of $\mathcal{O}((k+1)\log M)$ 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.