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

Richard G. Baraniuk

doi:10.1109/ICASSP.1994.390016

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

Richard G. Baraniuk

Research output: Contribution to journal › Conference article › peer-review

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

Original language	English (US)
Article number	390016
Pages (from-to)	III357-III360
Journal	ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume	3
DOIs	https://doi.org/10.1109/ICASSP.1994.390016
State	Published - 1994
Event	Proceedings of the 1994 IEEE International Conference on Acoustics, Speech and Signal Processing. Part 2 (of 6) - Adelaide, Aust Duration: Apr 19 1994 → Apr 22 1994

ASJC Scopus subject areas

Software
Signal Processing
Electrical and Electronic Engineering

Access to Document

10.1109/ICASSP.1994.390016

Cite this

@article{090e2eaaa87746cfabe8c896d37eb3c5,

title = "Beyond time-frequency analysis: Energy densities in one and many dimensions",

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 timefrequency and time-scale distributions.",

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

note = "Publisher Copyright: {\textcopyright} 1994 IEEE.; Proceedings of the 1994 IEEE International Conference on Acoustics, Speech and Signal Processing. Part 2 (of 6) ; Conference date: 19-04-1994 Through 22-04-1994",

year = "1994",

doi = "10.1109/ICASSP.1994.390016",

language = "English (US)",

volume = "3",

pages = "III357--III360",

journal = "ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings",

issn = "1520-6149",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

}

TY - JOUR

T1 - Beyond time-frequency analysis

T2 - Proceedings of the 1994 IEEE International Conference on Acoustics, Speech and Signal Processing. Part 2 (of 6)

AU - Baraniuk, Richard G.

PY - 1994

Y1 - 1994

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

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

UR - http://www.scopus.com/inward/record.url?scp=84944998681&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84944998681&partnerID=8YFLogxK

U2 - 10.1109/ICASSP.1994.390016

DO - 10.1109/ICASSP.1994.390016

M3 - Conference article

AN - SCOPUS:84944998681

SN - 1520-6149

VL - 3

SP - III357-III360

JO - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings

JF - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings

M1 - 390016

Y2 - 19 April 1994 through 22 April 1994

ER -

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

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this