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Unitary Equivalence: A New Twist on Signal Processing

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Title: Unitary Equivalence: A New Twist on Signal Processing
Author: Baraniuk, Richard G.; Jones, Douglas L.
Type: Journal Paper
Keywords: unitary transformation; signal analysis
Citation: R. G. Baraniuk and D. L. Jones, "Unitary Equivalence: A New Twist on Signal Processing," IEEE Transactions on Signal Processing, vol. 43, no. 10, pp. 2269-2282, 1995.
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 techniques 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.
Date Published: 1995-10-01

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  • ECE Publications [1082 items]
    Publications by Rice University Electrical and Computer Engineering faculty and graduate students
  • DSP Publications [508 items]
    Publications by Rice Faculty and graduate students in digital signal processing.