Joint Distributions for Arbitray Variables

Absf~act We compare the methods of Cohen and 2. REVIEW OF THE TWO METHODS of Baraniuk and Jones-for obtaining joint distributions for arbitrary variables. We show that the two methods produce identical results for variables whose associated operators are obtained via a unitary transformation of the time and frequency operators. In addition, we generalize this result and show that all pairs of variables connected by a unitary transformation have joint distributions that are identical in functional form. This result shows how pairs of variables can be grouped into classes whose joint distributions are functionally equivalent and, therefore, share equivalent properties.