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

9 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 - Jan 1 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

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

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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.

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