# Gabor frames and deep scattering networks in audio processing

## TL;DR

This paper presents Gabor scattering, a novel feature extraction method for audio signals that leverages Gabor frames and scattering transforms to achieve invariance and stability, improving performance especially with limited training data.

## Contribution

It introduces Gabor scattering, combining Gabor frames with scattering transforms, and analyzes its invariance and stability properties for audio processing.

## Key findings

- Gabor scattering provides invariance to spectral shape changes and frequency modulation.
- It demonstrates higher classification performance than Gabor transform alone.
- Numerical experiments confirm theoretical invariance and stability properties.

## Abstract

This paper introduces Gabor scattering, a feature extractor based on Gabor frames and Mallat's scattering transform. By using a simple signal model for audio signals specific properties of Gabor scattering are studied. It is shown that for each layer, specific invariances to certain signal characteristics occur. Furthermore, deformation stability of the coefficient vector generated by the feature extractor is derived by using a decoupling technique which exploits the contractivity of general scattering networks. Deformations are introduced as changes in spectral shape and frequency modulation. The theoretical results are illustrated by numerical examples and experiments. Numerical evidence is given by evaluation on a synthetic and a "real" data set, that the invariances encoded by the Gabor scattering transform lead to higher performance in comparison with just using Gabor transform, especially when few training samples are available.