# A differentiable short-time Fourier transform with respect to the window length

arXiv: https://arxiv.org/abs/2208.10886 · HTML: https://mlsanity.com/paper/2208.10886/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 19 references that are in the map.
- First posted on arXiv 23 Aug 2022.

## Builds on (most cited first, 4 of 4)

- [SpecAugment: A Simple Data Augmentation Method for Automatic Speech Recognition](https://mlsanity.com/paper/1904.08779/) (2019)
- [AST: Audio Spectrogram Transformer](https://mlsanity.com/paper/2104.01778/) (2021)
- [Hybrid Spectrogram and Waveform Source Separation](https://mlsanity.com/paper/2111.03600/) (2021)
- [Optimizing Short-Time Fourier Transform Parameters via Gradient Descent](https://mlsanity.com/paper/2010.15049/) (2020)

## Built on by (most cited first, 4 of 4)

- [Differentiable adaptive short-time Fourier transform with respect to the window length](https://mlsanity.com/paper/2308.02418/) (2023)
- [Differentiable short-time Fourier transform with respect to the hop length](https://mlsanity.com/paper/2308.02421/) (2023)
- [Toward end-to-end interpretable convolutional neural networks for waveform signals](https://mlsanity.com/paper/2405.01815/) (2024)
- [Learnable Adaptive Time-Frequency Representation via Differentiable Short-Time Fourier Transform](https://mlsanity.com/paper/2506.21440/) (2025)

## Abstract (arXiv)

In this paper, we revisit the use of spectrograms in neural networks, by making the window length a continuous parameter optimizable by gradient descent instead of an empirically tuned integer-valued hyperparameter. The contribution is mostly theoretical at this point, but plugging the modified STFT into any existing neural network is straightforward. We first define a differentiable version of the STFT in the case where local bins centers are fixed and independent of the window length parameter. We then discuss the more difficult case where the window length affects the position and number of bins. We illustrate the benefits of this new tool on an estimation and a classification problems, showing it can be of interest not only to neural networks but to any STFT-based signal processing algorithm.