Covariant time-frequency representations through unitary equivalence

Richard G. Baraniuk

doi:10.1109/97.481161

Covariant time-frequency representations through unitary equivalence

Richard G. Baraniuk

Houston Methodist

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

We propose a straightforward characterization of all quadratic time-frequency representations covariant to an important class of unitary signal transforms (namely, those having two continuous-valued parameters and an underlying group structure). Thanks to a fundamental theorem from the theory of Lie groups, we can describe these representations simply in terms of unitary transformations of the well-known Cohen's and affine classes.

Original language	English (US)
Pages (from-to)	79-81
Number of pages	3
Journal	IEEE Signal Processing Letters
Volume	3
Issue number	3
DOIs	https://doi.org/10.1109/97.481161
State	Published - Mar 1996

ASJC Scopus subject areas

Signal Processing
Electrical and Electronic Engineering
Applied Mathematics

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10.1109/97.481161

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title = "Covariant time-frequency representations through unitary equivalence",

abstract = "We propose a straightforward characterization of all quadratic time-frequency representations covariant to an important class of unitary signal transforms (namely, those having two continuous-valued parameters and an underlying group structure). Thanks to a fundamental theorem from the theory of Lie groups, we can describe these representations simply in terms of unitary transformations of the well-known Cohen's and affine classes.",

author = "Baraniuk, \{Richard G.\}",

note = "Funding Information: Manuscript received June 13, 1995. This work was supported by the National Science Foundation under Grant MIP-9457438, by the Office of Naval Research under Grant NOOO14-951-0849, and by the Texas Advanced Technology Program under Grant TX-ATP 003604-002. The associate editor coordinating the review of this letter and approving it for publication was Prof. D. L. Jones.",

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PY - 1996/3

Y1 - 1996/3

N2 - We propose a straightforward characterization of all quadratic time-frequency representations covariant to an important class of unitary signal transforms (namely, those having two continuous-valued parameters and an underlying group structure). Thanks to a fundamental theorem from the theory of Lie groups, we can describe these representations simply in terms of unitary transformations of the well-known Cohen's and affine classes.

AB - We propose a straightforward characterization of all quadratic time-frequency representations covariant to an important class of unitary signal transforms (namely, those having two continuous-valued parameters and an underlying group structure). Thanks to a fundamental theorem from the theory of Lie groups, we can describe these representations simply in terms of unitary transformations of the well-known Cohen's and affine classes.

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Covariant time-frequency representations through unitary equivalence

Abstract

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