ON JOINT DISTRIBUTIONS OF ARBITRARY VARIABLES


Richard G. Baraniuk 

  Department of Electrical and Computer Engineering
  Rice University
  Houston, TX 77251-1892

Leon Cohen
  Hunter College and Graduate Center
  City University of New York
  New York, NY 10021


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.