Joint distributions for arbitrary variables

Leon Cohen; Richard G. Baraniuk

Joint distributions for arbitrary variables

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

We compare the methods of Cohen and of Baraniuk and Jones for obtaining joint distributions for arbitrary variables. We show that the two methods produce identical results for variables whose associated operators are obtained via a unitary transformation of the time and frequency operators. In addition, we generalize this result and show that all pairs of variables connected by a unitary transformation have joint distributions that are identical in functional form. This result shows how pairs of variables can be grouped into classes whose joint distributions are functionally equivalent and, therefore, share equivalent properties.

Original language	English
Title of host publication	Unknown Host Publication Title
Editors	Anon
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	520-523
Number of pages	4
State	Published - Dec 1 1994
Event	Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis - Philadelphia, PA, USA Duration: Oct 25 1994 → Oct 28 1994

Other

Other	Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis
City	Philadelphia, PA, USA
Period	10/25/94 → 10/28/94

ASJC Scopus subject areas

Engineering(all)

Cite this

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title = "Joint distributions for arbitrary variables",

abstract = "We compare the methods of Cohen and of Baraniuk and Jones for obtaining joint distributions for arbitrary variables. We show that the two methods produce identical results for variables whose associated operators are obtained via a unitary transformation of the time and frequency operators. In addition, we generalize this result and show that all pairs of variables connected by a unitary transformation have joint distributions that are identical in functional form. This result shows how pairs of variables can be grouped into classes whose joint distributions are functionally equivalent and, therefore, share equivalent properties.",

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N2 - We compare the methods of Cohen and of Baraniuk and Jones for obtaining joint distributions for arbitrary variables. We show that the two methods produce identical results for variables whose associated operators are obtained via a unitary transformation of the time and frequency operators. In addition, we generalize this result and show that all pairs of variables connected by a unitary transformation have joint distributions that are identical in functional form. This result shows how pairs of variables can be grouped into classes whose joint distributions are functionally equivalent and, therefore, share equivalent properties.

AB - We compare the methods of Cohen and of Baraniuk and Jones for obtaining joint distributions for arbitrary variables. We show that the two methods produce identical results for variables whose associated operators are obtained via a unitary transformation of the time and frequency operators. In addition, we generalize this result and show that all pairs of variables connected by a unitary transformation have joint distributions that are identical in functional form. This result shows how pairs of variables can be grouped into classes whose joint distributions are functionally equivalent and, therefore, share equivalent properties.

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M3 - Conference contribution

AN - SCOPUS:0028713033

SP - 520

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BT - Unknown Host Publication Title

A2 - Anon, null

PB - Institute of Electrical and Electronics Engineers Inc.

Y2 - 25 October 1994 through 28 October 1994

ER -

Joint distributions for arbitrary variables

Abstract

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ASJC Scopus subject areas

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Cite this