A current controversy in machine learning for audio using neural networks concerns the way input signals are handled. The more classical approaches involve pre-processing the signals using time-frequency representations, while more recently end-to-end approaches are applied, where the manual pre-processing step is skipped and the networks use the raw signals directly. 

Parametric approaches like SincNet or LEAF, where parameters of a filterbank are learned together with the rest of the network parameters, embody the idea of removing human involvement by means of manual feature crafting as much as possible while still using the benefits of representations that are based on domain knowledge.

In this project we investigate hybrid filterbanks, another approach to represent audio signals in the context of machine learning. These filterbanks comprise compositions of fixed filters and learned kernels:

A hybrid filterbank $(\mathbf{W}\circledast\boldsymbol{\Psi})$ composes $J$ non-learnable filters $\boldsymbol{\Psi}=(\boldsymbol{\psi}_j)_{j=0}^{J-1}$ where $\boldsymbol{\psi}_j \in \mathbb{C}^N$ with $J$ learnable filters $\mathbf{W}=(\boldsymbol{w}_j)_{j=0}^{J-1}$ where $\boldsymbol{w}_j \in \mathbb{R}^T$, $T \le N$, for every filter index $j$ by convolution.

We investigate the mathematical, signal processing and machine learning properties of such an approach, and apply it to acoustical applications.

This project is closely related to the project StruMoDeep, and the ANR project "Multi-Resolution Neural Networks".