Covariant Time-Frequency Representations Through Unitary Equivalence


Richard G. Baraniuk
Department of Electrical and Computer Engineering
Rice University
Houston, TX 77251-1892, USA
Email: richb@rice.edu


We propose a straightforward characterization of all quadratic
time-frequency representations covariant to an important class of
unitary signal transforms (namely, those having two continuous-valued
parameters and an underlying group structure).  Thanks to a
fundamental theorem from the theory of Lie groups, we can describe
these representations simply in terms of unitary transformations of
the well-known Cohen's and affine classes.


Submitted to IEEE Signal Processing Letters  19 June 1995