BEYOND TIME-FREQUENCY ANALYSIS:  
  ENERGY DENSITIES IN ONE AND MANY DIMENSIONS


Richard G. Baraniuk
Department of Electrical and Computer Engineering
Rice University
Houston, TX 77251--1892, USA
Email: richb@rice.edu


Given a unitary operator  A  representing a physical quantity 
of interest, we employ concepts from group representation theory 
to define two natural signal energy densities for  A.  The first 
is invariant to  A  and proves useful when the effect of  A  is
to be ignored; the second is covariant to  A  and measures the 
``A'' content of signals.  The construction is quite general and 
is also easily extended to the multi-operator case, which 
generalizes previously derived joint densities such as the 
time-frequency and time-scale distributions.


Presented at IEEE ICASSP 1994, Adelaide, Australia