Beyond time-frequency analysis: energy densities in one and many dimensions

Richard G. Baraniuk

doi:10.1109/78.709511

Beyond time-frequency analysis: energy densities in one and many dimensions

Richard G. Baraniuk

Houston Methodist

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

17 Scopus citations

Abstract

Given a unitary operator A representing a physical quantity of interest, we employ concepts from group representation theory to define two natural signal energy densities for A. The first is invariant to A and proves useful when the effect of A is to be ignored; the second is covariant to A and measures the "A" content of signals. We also consider joint densities for multiple operators and, in the process, provide an alternative interpretation of Cohen's general construction for joint distributions of arbitrary variables.

Original language	English (US)
Pages (from-to)	2305-2314
Number of pages	10
Journal	IEEE Transactions on Signal Processing
Volume	46
Issue number	9
DOIs	https://doi.org/10.1109/78.709511
State	Published - 1998

ASJC Scopus subject areas

Signal Processing
Electrical and Electronic Engineering

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10.1109/78.709511

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abstract = "Given a unitary operator A representing a physical quantity of interest, we employ concepts from group representation theory to define two natural signal energy densities for A. The first is invariant to A and proves useful when the effect of A is to be ignored; the second is covariant to A and measures the {"}A{"} content of signals. We also consider joint densities for multiple operators and, in the process, provide an alternative interpretation of Cohen's general construction for joint distributions of arbitrary variables.",

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

note = "Funding Information: Manuscript received November 13, 1996; revised January 13, 1998. This work was supported by the National Science Foundation under Grant MIP-9457438 and the Office of Naval Research under Grant N00014-95-1-0849. The associate editor coordinating the review of this paper and approving it for publication was Dr. Akram Aldroubi.",

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N1 - Funding Information: Manuscript received November 13, 1996; revised January 13, 1998. This work was supported by the National Science Foundation under Grant MIP-9457438 and the Office of Naval Research under Grant N00014-95-1-0849. The associate editor coordinating the review of this paper and approving it for publication was Dr. Akram Aldroubi.

PY - 1998

Y1 - 1998

N2 - Given a unitary operator A representing a physical quantity of interest, we employ concepts from group representation theory to define two natural signal energy densities for A. The first is invariant to A and proves useful when the effect of A is to be ignored; the second is covariant to A and measures the "A" content of signals. We also consider joint densities for multiple operators and, in the process, provide an alternative interpretation of Cohen's general construction for joint distributions of arbitrary variables.

AB - Given a unitary operator A representing a physical quantity of interest, we employ concepts from group representation theory to define two natural signal energy densities for A. The first is invariant to A and proves useful when the effect of A is to be ignored; the second is covariant to A and measures the "A" content of signals. We also consider joint densities for multiple operators and, in the process, provide an alternative interpretation of Cohen's general construction for joint distributions of arbitrary variables.

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Beyond time-frequency analysis: energy densities in one and many dimensions

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