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

Author

Baraniuk, Richard G.

Author_Institution

Dept. of Electr. & Comput. Eng., Rice Univ., Houston, TX, USA

Volume

46

Issue

9

fYear

1998

fDate

9/1/1998 12:00:00 AM

Firstpage

2305

Lastpage

2314

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 (see Englewood Cliffs, NJ: Prentice-Hall, 1995) general construction for joint distributions of arbitrary variables

Keywords

group theory; mathematical operators; signal representation; statistical analysis; time-frequency analysis; Cohen´s method; Hermitian operators; arbitrary variables; energy content; group representation theory; joint densities; joint distributions; multiple operators; natural signal energy densities; signal processing; signal representation; time-frequency analysis; unitary operator; Geophysical measurements; Radar applications; Radar signal processing; Signal analysis; Signal processing; Signal representations; Speech analysis; Speech processing; Time frequency analysis; Transient analysis;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.709511

Filename

709511