UNITARY EQUIVALENCE:  A NEW TWIST ON SIGNAL PROCESSING

Richard G. Baraniuk and Douglas L. Jones

Department of Electrical and Computer Engineering
Rice University
Houston, TX 77251-1892

Department of Electrical and Computer Engineering
University of Illinois
Urbana, IL 61801

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.

To appear in IEEE Transactions on Signal Processing.