Gabor frames and deep scattering networks in audio processing
This work addresses audio signal processing by developing a theoretically grounded feature extractor, though it appears incremental as it builds on existing scattering network frameworks.
The paper introduces Gabor scattering, a feature extractor combining Gabor frames and scattering transforms for audio processing, showing that it encodes invariances to spectral shape and frequency modulation deformations. Numerical experiments on synthetic and real datasets demonstrate that it outperforms Gabor transforms, particularly with limited training samples.
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.