A SIMPLE COVARIANCE-BASED CHARACTERIZATION OF JOINT 
SIGNAL REPRESENTATIONS OF ARBITRARY VARIABLES             

Akbar M. Sayeed and Douglas L. Jones

Coordinated Science Laboratory
University of Illinois
Urbana, IL 61801

1996 IEEE International Symposium on Time-Frequency and 
Time-Scale Analysis, Paris, France   

ABSTRACT:

Joint signal representations of arbitrary variables extend the scope of 
joint time-frequency representations, and provide a useful description for 
a wide variety of nonstationary signal characteristics.  Cohen's 
marginal-based theory for bilinear representations is canonical from a 
distributional viewpoint, whereas, from other perspectives, such as 
characterization of the effect of unitary signal transformations of 
interest, a covariance-based formulation is needed and more attractive. 
In this paper, we present a simple covariance-based characterization of 
bilinear joint signal representations of arbitrary variables.  The 
formulation is highlighted by its simple structure and interpretation, 
and naturally extends the concept of the corresponding linear 
representations.