Regularity and unitarity of affine and hyperbolic time-frequency representations

Franz Hlawatsch, Antonia Papandreou, G. Faye Boudreaux-Bartels

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

10 Scopus citations

Abstract

The affine and hyperbolic classes of quadratic time-frequency representations (QTFRs) provide frameworks for multiresolution or constant-Q time-frequency analysis. This paper studies the QTFR properties of regularity (QTFR reversibility) and unitarity (preservation of inner products, Moyal's formula) in the context of affine and hyperbolic QTFRs. We develop the calculus of inverse kernels and discuss important implications of regularity and unitarity, such as signal recovery, the derivation of other quadratic signal representations, optimum detection, least-squares signal synthesis, the effect of linear signal transforms, and the construction of QTFR basis systems.

Original languageEnglish (US)
Title of host publicationDigital Speech Processing
PublisherPubl by IEEE
Pages111.245-248
ISBN (Print)0780309464
StatePublished - Jan 1 1993
Externally publishedYes
Event1993 IEEE International Conference on Acoustics, Speech and Signal Processing - Minneapolis, MN, USA
Duration: Apr 27 1993Apr 30 1993

Publication series

NameProceedings - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing
Volume3
ISSN (Print)0736-7791

Other

Other1993 IEEE International Conference on Acoustics, Speech and Signal Processing
CityMinneapolis, MN, USA
Period4/27/934/30/93

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

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