New signal-space orthonormal bases via the metaplectic transform

Richard G. Baraniuk; D. L. Jones

doi:10.1109/TFTSA.1992.274169

New signal-space orthonormal bases via the metaplectic transform

Richard G. Baraniuk, D. L. Jones

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English (US)
Title of host publication	Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	339-342
Number of pages	4
ISBN (Electronic)	0780308050, 9780780308053
DOIs	https://doi.org/10.1109/TFTSA.1992.274169
State	Published - Jan 1 1992
Event	1992 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis - Victoria, Canada Duration: Oct 4 1992 → Oct 6 1992

Other

Other	1992 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis
Country	Canada
City	Victoria
Period	10/4/92 → 10/6/92

ASJC Scopus subject areas

Signal Processing

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10.1109/TFTSA.1992.274169

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Baraniuk, RG & Jones, DL 1992, New signal-space orthonormal bases via the metaplectic transform. in Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis., 274169, Institute of Electrical and Electronics Engineers Inc., pp. 339-342, 1992 IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, Victoria, Canada, 10/4/92. https://doi.org/10.1109/TFTSA.1992.274169

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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.",

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