Unitary Equivalence: A New Twist on Signal Processing

Richard G. Baraniuk, Douglas L. Jones

Research output: Contribution to journalArticlepeer-review

178 Scopus citations

Abstract

Unitary similarity transformations furnish a powerful vehicle for generating infinite generic classes of signal analysis and processing tools based on concepts different from time, frequency, and scale. Implementation of these new tools involves simply preprocessing the signal by a unitary transformation, performing standard processing on the transformed signal, and then (in some cases) transforming the resulting output. The resulting unitarily equivalent systems can focus on the critical signal characteristics in large classes of signals and, hence, prove useful for representing and processing signals that are not well matched by current techniques. As specific examples of this procedure, we generalize linear time-invariant systems, orthonormal basis and frame decompositions, and joint time-frequency and time-scale distributions. These applications illustrate the utility of the unitary equivalence concept for uniting seemingly disparate approaches proposed in the literature.

Original languageEnglish (US)
Pages (from-to)2269-2282
Number of pages14
JournalIEEE Transactions on Signal Processing
Volume43
Issue number10
DOIs
StatePublished - Dec 1995

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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