Differentiable short-time Fourier transform with respect to the hop length

TL;DR

This paper introduces a differentiable short-time Fourier transform (STFT) that allows for gradient-based optimization of hop length, enabling more precise control over temporal framing in signal processing and neural network applications.

Contribution

The paper presents a novel differentiable STFT that makes hop length continuous, facilitating gradient-based optimization and integration into neural networks.

Findings

Enables gradient-based optimization of hop length.

Improves control over frame positioning.

Demonstrates efficacy through simulation.

Abstract

In this paper, we propose a differentiable version of the short-time Fourier transform (STFT) that allows for gradient-based optimization of the hop length or the frame temporal position by making these parameters continuous. Our approach provides improved control over the temporal positioning of frames, as the continuous nature of the hop length allows for a more finely-tuned optimization. Furthermore, our contribution enables the use of optimization methods such as gradient descent, which are more computationally efficient than conventional discrete optimization methods. Our differentiable STFT can also be easily integrated into existing algorithms and neural networks. We present a simulated illustration to demonstrate the efficacy of our approach and to garner interest from the research community.