A LIMITATION OF THE KERNEL METHOD FOR JOINT DISTRIBUTIONS
 OF ARBITRARY VARIABLES


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 construction for joint distributions of
arbitrary physical quantities, in direct generalization of joint
time-frequency representations.  Actually this method encompasses two
approaches, one based on operator correspondences and one based on
weighting kernels.  The literature has emphasized the kernel method
due to its ease of analysis; however, its simplicity comes at a price.
In this paper, we use a simple example to demonstrate that the kernel
method cannot generate all possible bilinear joint distributions.  Our
results suggest that the relationship between the operator method and
the kernel method merits closer scrutiny.


To appear in IEEE Signal Processing Letters  1996