An Adaptive Optimal-Kernel Time-Frequency Representation
	 Douglas L. Jones and Richard G. Baraniuk 

          IEEE Transactions on Signal Processing
       Vol. 43, No. 11, pp. 2361-2371, October 1995


	    	       ABSTRACT

Time-frequency representations with fixed windows or kernels 
figure prominently in many applications, but perform well only 
for limited classes of signals.  Representations with signal-
dependent kernels can overcome this limitation.  However, while 
they often perform well, most existing schemes are block-oriented 
techniques unsuitable for on-line implementation or for tracking
signal components with characteristics that change with time.  
The time-frequency representation developed here, based on a 
signal-dependent radially Gaussian kernel that adapts over time, 
overcomes these limitations.  The method employs a short-time 
ambiguity function both for kernel optimization and as an 
intermediate step in computing constant-time slices of the 
representation.  Careful algorithm design provides reasonably
efficient computation and allows on-line implementation.  Certain 
enhancements, such as cone-kernel constraints and approximate 
retention of marginals, are easily incorporated with little
additional computation.  While somewhat more expensive than 
fixed-kernel representations, this new technique often provides 
much better performance.  Several examples illustrate its 
behavior on synthetic and real-world signals.

Email: richb@rice.edu