On Joint Distributions for Arbitrary Variables
Baraniuk, Richard G.
There has been considerable interest in the problem of joint representations for variables other than time and frequency. In this letter we compare the methods of Cohen and of Baraniuk and Jones and show their equivalence for variables that have the same commutator as time and frequency. In addition we report the following very general result: all pairs of variables connected by a unitary transformation have joint distributions that are functionally equivalent.