Optimizing Short-Time Fourier Transform Parameters via Gradient Descent

TL;DR

This paper introduces a gradient-based method to optimize STFT parameters such as window length and hop size, including dynamic adjustments over time, improving signal processing tasks.

Contribution

It presents a novel approach to compute gradients of STFT parameters with respect to arbitrary cost functions, enabling gradient descent optimization for both static and dynamic parameter settings.

Findings

Gradient computation for STFT parameters enables optimization.

Dynamic parameter adjustment improves signal analysis.

Method enhances STFT's adaptability to varying signals.

Abstract

The Short-Time Fourier Transform (STFT) has been a staple of signal processing, often being the first step for many audio tasks. A very familiar process when using the STFT is the search for the best STFT parameters, as they often have significant side effects if chosen poorly. These parameters are often defined in terms of an integer number of samples, which makes their optimization non-trivial. In this paper we show an approach that allows us to obtain a gradient for STFT parameters with respect to arbitrary cost functions, and thus enable the ability to employ gradient descent optimization of quantities like the STFT window length, or the STFT hop size. We do so for parameter values that stay constant throughout an input, but also for cases where these parameters have to dynamically change over time to accommodate varying signal characteristics.