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

iii

fYear

1994

fDate

19-22 Apr 1994

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. The construction is quite general and is also easily extended to the multi-operator case, which generalizes previously derived joint densities such as the time-frequency and time-scale distributions

Keywords

group theory; signal representation; statistical analysis; time-frequency analysis; covariant signal energy densities; group representation theory; invariant signal energy densities; joint densities; time-frequency analysis; time-frequency distributions; time-scale distributions; unitary operator; Density measurement; Eigenvalues and eigenfunctions; Energy measurement; Radar applications; Radar signal processing; Signal analysis; Signal processing; Speech analysis; Speech processing; Time frequency analysis;

fLanguage

English

Publisher

ieee

Conference_Titel

Acoustics, Speech, and Signal Processing, 1994. ICASSP-94., 1994 IEEE International Conference on

Conference_Location

Adelaide, SA

ISSN

1520-6149

Print_ISBN

0-7803-1775-0

Type

conf

DOI

10.1109/ICASSP.1994.390016

Filename

390016