Phase-Based Signal Representations for Scattering
This work addresses signal processing challenges for audio analysis, but it appears incremental as it extends existing scattering methods with phase-based modifications.
The paper tackles the problem of representing large-scale structures in signals by introducing phase scattering, a novel approach that uses phase derivatives in a scattering transform, leading to well-localized signal representations.
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.