One or two frequencies? The scattering transform answers

Vincent Lostanlen, Alice Cohen-Hadria, Juan Pablo Bello

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

With the aim of constructing a biologically plausible model of machine listening, we study the representation of a multicomponent stationary signal by a wavelet scattering network. First, we show that renormalizing second-order nodes by their first-order parents gives a simple numerical criterion to assess whether two neighboring components will interfere psychoacoustically. Secondly, we run a manifold learning algorithm (Isomap) on scattering coefficients to visualize the similarity space underlying parametric additive synthesis. Thirdly, we generalize the “one or two components” framework to three sine waves or more, and prove that the effective scattering depth of a Fourier series grows in logarithmic proportion to its bandwidth.

Original languageEnglish (US)
Title of host publication28th European Signal Processing Conference, EUSIPCO 2020 - Proceedings
PublisherEuropean Signal Processing Conference, EUSIPCO
Pages2205-2209
Number of pages5
ISBN (Electronic)9789082797053
DOIs
StatePublished - Jan 24 2021
Event28th European Signal Processing Conference, EUSIPCO 2020 - Amsterdam, Netherlands
Duration: Aug 24 2020Aug 28 2020

Publication series

NameEuropean Signal Processing Conference
Volume2021-January
ISSN (Print)2219-5491

Conference

Conference28th European Signal Processing Conference, EUSIPCO 2020
CountryNetherlands
CityAmsterdam
Period8/24/208/28/20

Keywords

  • Amplitude modulation
  • Audio systems
  • Continuous wavelet transform
  • Fourier series
  • Multi-layer neural network

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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