Phase-Based Signal Representations for Scattering

TL;DR

This paper introduces phase scattering, a novel signal representation method that uses phase derivatives within a scattering transform framework to achieve well-localized representations of large-scale structures in signals.

Contribution

It extends the scattering transform by incorporating phase derivatives, providing a new approach to time-frequency signal representation.

Findings

Phase derivatives effectively capture time-frequency information.

Phase scattering improves localization of large-scale structures.

The method is demonstrated using the STFT.

Abstract

The scattering transform is a non-linear signal representation method based on cascaded wavelet transform magnitudes. In this paper we introduce phase scattering, a novel approach where we use phase derivatives in a scattering procedure. We first revisit phase-related concepts for representing time-frequency information of audio signals, in particular, the partial derivatives of the phase in the time-frequency domain. By putting analytical and numerical results in a new light, we set the basis to extend the phase-based representations to higher orders by means of a scattering transform, which leads to well localized signal representations of large-scale structures. All the ideas are introduced in a general way and then applied using the STFT.