On Joint Distributions for Arbitrary Variables

Richard G. Baraniuk; Leon Cohen

doi:10.1109/97.365519

On Joint Distributions for Arbitrary Variables

Richard G. Baraniuk, Leon Cohen

Houston Methodist

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

26 Scopus citations

Abstract

There has been considerable interest in the problem of joint representations for variables other than time and frequency. In this letter, we compare the methods of Cohen and of Baraniuk and Jones and show their equivalence for variables that have the same commutator as time and frequency. In addition, we report the following very general result: All pairs of variables connected by a unitary transformation have joint distributions that are functionally equivalent.

Original language	English (US)
Pages (from-to)	10-12
Number of pages	3
Journal	IEEE Signal Processing Letters
Volume	2
Issue number	1
DOIs	https://doi.org/10.1109/97.365519
State	Published - Jan 1995

ASJC Scopus subject areas

Signal Processing
Electrical and Electronic Engineering
Applied Mathematics

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title = "On Joint Distributions for Arbitrary Variables",

abstract = "There has been considerable interest in the problem of joint representations for variables other than time and frequency. In this letter, we compare the methods of Cohen and of Baraniuk and Jones and show their equivalence for variables that have the same commutator as time and frequency. In addition, we report the following very general result: All pairs of variables connected by a unitary transformation have joint distributions that are functionally equivalent.",

author = "Baraniuk, {Richard G.} and Leon Cohen",

note = "Funding Information: Manuscript received June 13, 1994; approved September 27. 1994. This work was supported by the Texas Advanced Technology Program, the NSA HBCU/MI program, and the PSC-CUNY Research Award Program. The assosciate editor coordinating the review of this letter and approving it for publication was Prof. G. F. Boudreaux-Bartels. R. Baraniuk is with the Department of Electrical and Computer Engineering, Rice University, Houston, TX 77005 USA. L. Cohen is with Hunter College and Graduate Center of CUNY, New York, NY 10021 USA. IEEE Log Number 9408346.",

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N2 - There has been considerable interest in the problem of joint representations for variables other than time and frequency. In this letter, we compare the methods of Cohen and of Baraniuk and Jones and show their equivalence for variables that have the same commutator as time and frequency. In addition, we report the following very general result: All pairs of variables connected by a unitary transformation have joint distributions that are functionally equivalent.

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On Joint Distributions for Arbitrary Variables

Abstract

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