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

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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 flrst 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. In the process, we provide an alternative interpretation of Cohen's general construction for joint distributions of arbitrary variables.

Original languageEnglish (US)
Number of pages1
JournalIEEE Transactions on Signal Processing
Volume45
Issue number3
StatePublished - Dec 1 1997

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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