UNITARY EQUIVALENCE - A NEW TWIST ON SIGNAL-PROCESSING

Unitary similarity transformations furnish a powerful vehicle for gene rating infinite generic classes of signal analysis and processing tool s based on concepts different from time, frequency, and scale. Impleme ntation of these new tools involves simply preprocessing the signal by a unitary transformation, performing standard processing on the trans formed signal, and then (in some cases) transforming the resulting out put. The resulting unitarily equivalent systems can focus on the criti cal signal characteristics in large classes of signals and, hence, pro ve useful for representing and processing signals that are not well ma tched by current techniques. As specific examples of this procedure, w e generalize linear time-invariant systems, orthonormal basis and fram e decompositions, and joint time-frequency and timescale distributions . These applications illustrate the utility of the unitary equivalence concept for uniting seemingly disparate approaches proposed in the li terature.