JOINT DISTRIBUTIONS OF ARBITRARY VARIABLES MADE EASY


Richard G. Baraniuk 

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


Suubmitted to  Multidimensional Systems and Signal Processing 
              (Special issue on time-frequency analysis), 
	       August 1996.   Also appears in the Proceedings 
	       of the IEEE Dignal Signal Processing Workshop, 
	       Loen, Norway, pp. 394-397, September 1996.


In this paper, we propose a simple framework for studying certain
distributions of variables beyond time-frequency and time-scale.  When
applicable, our results turn the theory of joint distributions of
arbitrary variables into an easy exercise of coordinate
transformation.  While straightforward, the method can generate many
distributions previously attainable only by the general construction
of Cohen, including time versus inverse frequency, time versus Mellin
transform (scale), and time versus chirp distributions.  In addition
to providing insight into these new signal analysis tools, warp-based
distributions have efficient implementations for potential use in
applications.