Marginals vs. Covariance in Joint Distribution Theory
Baraniuk, Richard G.
covariance properties; joint time-frequency representations
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.