MARGINALS vs. COVARIANCE IN JOINT DISTRIBUTION THEORY

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


Recently, Cohen has proposed a method for constructing joint
distributions of arbitrary physical quantities, in direct
generalization of joint time-frequency representations.  In this
paper, we investigate the covariance properties of this procedure 
and caution that in its present form it cannot generate all possible
distributions.  Using group theory, we extend Cohen's construction 
to a more general form that can be customized to satisfy specific
marginal and covariance requirements.


Presented at ICASSP 1995 in Detroit, MI, May 1995.

Note: The electronic version of this paper has been modified to be
      more readable and therefore differs from the Proceedings 
      version.