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 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 general construction for joint distributions of arbitrary variables.

Original languageEnglish (US)
Pages (from-to)2305-2314
Number of pages10
JournalIEEE Transactions on Signal Processing
Volume46
Issue number9
DOIs
StatePublished - 1998

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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