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A New Generalized Projection and Its Application to Acceleration of Audio Declipping
Open AccessArticle

Gabor Frames and Deep Scattering Networks in Audio Processing

1
NuHAG, Faculty of Mathematics, University of Vienna, 1090 Wien, Austria
2
Department of Telecommunications, Brno University of Technology, 60190 Brno, Czech Republic
*
Author to whom correspondence should be addressed.
Axioms 2019, 8(4), 106; https://doi.org/10.3390/axioms8040106
Received: 16 April 2019 / Revised: 5 September 2019 / Accepted: 20 September 2019 / Published: 26 September 2019
(This article belongs to the Special Issue Harmonic Analysis and Applications)
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” dataset, 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. View Full-Text
Keywords: machine learning; scattering transform; Gabor transform; deep learning; time-frequency analysis; CNN machine learning; scattering transform; Gabor transform; deep learning; time-frequency analysis; CNN
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Bammer, R.; Dörfler, M.; Harar, P. Gabor Frames and Deep Scattering Networks in Audio Processing. Axioms 2019, 8, 106.

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