Oscillatory + transient signal decomposition using overcomplete rational-dilation wavelet transforms

Ivan W. Selesnick, Ïlker Bayram

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

Abstract

This paper describes an approach for decomposing a signal into the sum of an oscillatory component and a transient component. The method uses a newly developed rational-dilation wavelet transform (WT), a selfinverting constant-Q transform with an adjustable Q-factor (quality-factor). We propose that the oscillatory component be modeled as signal that can be sparsely represented using a high Q-factor WT; likewise, we propose that the transient component be modeled as a piecewise smooth signal that can be sparsely represented using a low Q-factor WT. Because the low and high Q-factor wavelet transforms are highly distinct (having low coherence), morphological component analysis (MCA) successfully yields the desired decomposition of a signal into an oscillatory and non-oscillatory component. The method, being non-linear, is not constrained by the limits of conventional LTI filtering.

Original languageEnglish (US)
Title of host publicationWavelets XIII
DOIs
StatePublished - 2009
EventWavelets XIII - San Diego, CA, United States
Duration: Aug 2 2009Aug 4 2009

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
Volume7446
ISSN (Print)0277-786X

Other

OtherWavelets XIII
CountryUnited States
CitySan Diego, CA
Period8/2/098/4/09

Keywords

  • Constant Q
  • Morphological component analysis
  • Q-factor
  • Sparsity
  • Wavelets

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering

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