New signal-space orthonormal bases via the metaplectic transform

Richard G. Baraniuk, D. L. Jones

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

8 Scopus citations

Abstract

The two primary classes of time-frequency-concentrated orthonormal bases (ONBs) can be interpreted a8 arising from the discretization of either the short-time Fourier tranaform (STFT) or the continuous wavelet transform (CWT). Recently, the five-dimensional metaplectic transform (MT) has been proposed as a generalization of the STFT and CWT. It allows shears and rotations of the analyzing window/ wavelet in the time-frequency plane, in addition to translations and scaling. Just as the CWT and STFT can be discretized on lattices of points in two dimensions, the MT can be discretized on lattices of points in five dimensions. In this paper, we consider the discretization of the MT, and show that it can lead to entirely new ONBs for the signal space of square integrable functions. Two new classes of bases, the scale and shear bases and the translation and shear bases, are derived to demonstrate the discretization process. Besides generalizing the current methods of generating time-frequency-concentrated ONBs, MT bases possess extra degrees of freedom that can be used to match a wider variety of signals.

Original languageEnglish (US)
Title of host publicationProceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages339-342
Number of pages4
ISBN (Electronic)0780308050, 9780780308053
DOIs
StatePublished - Jan 1 1992
Event1992 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis - Victoria, Canada
Duration: Oct 4 1992Oct 6 1992

Other

Other1992 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis
CountryCanada
CityVictoria
Period10/4/9210/6/92

ASJC Scopus subject areas

  • Signal Processing

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