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

arXiv: https://arxiv.org/abs/2308.02421 · HTML: https://mlsanity.com/paper/2308.02421/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 26 references that are in the map.
- First posted on arXiv 26 Jul 2023.

## Builds on (most cited first, 5 of 5)

- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [Convolutional Recurrent Neural Networks for Music Classification](https://mlsanity.com/paper/1609.04243/) (2016)
- [Recurrent Neural Networks for Polyphonic Sound Event Detection in Real Life Recordings](https://mlsanity.com/paper/1604.00861/) (2016)
- [Optimizing Short-Time Fourier Transform Parameters via Gradient Descent](https://mlsanity.com/paper/2010.15049/) (2020)
- [A differentiable short-time Fourier transform with respect to the window length](https://mlsanity.com/paper/2208.10886/) (2022)

## Built on by (most cited first, 1 of 1)

- [Learnable Adaptive Time-Frequency Representation via Differentiable Short-Time Fourier Transform](https://mlsanity.com/paper/2506.21440/) (2025)

## Abstract (arXiv)

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.