Signal-Dependent Time-Frequency Analysis using a Radially Gaussian Kernel

Richard G. Baraniuk

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

Douglas L. Jones
  Department of Electrical and Computer Engineering
  University of Illinois
  Urbana, IL 61801


Appears in Signal Processing, vol. 32, no. 3, pp. 263-284,
  June 1993.


                       Abstract
					
Time-frequency distributions are two-dimensional functions that
indicate the time-varying frequency content of one-dimensional
signals.  Each bilinear time-frequency distribution corresponds to a
kernel function that controls its cross-component suppression
properties.  Current distributions rely on fixed kernels, which limit
the class of signals for which a given distribution performs well.  In
this paper, we propose a signal-dependent kernel that changes shape
for each signal to offer improved time-frequency representation for a
large class of signals.  The kernel design procedure is based on
quantitative optimization criteria and two-dimensional functions that
are Gaussian along radial profiles.  We develop an efficient scheme
based on Newton's algorithm for finding the optimal kernel; the cost
of computing the signal-dependent time-frequency distribution is close
to that of fixed-kernel methods.  Examples using both synthetic and
real-world multi-component signals demonstrate the effectiveness of
the signal-dependent approach -- even in the presence of substantial
additive noise.  An attractive feature of this technique is the ease
with which application-specific knowledge can be incorporated into the
kernel design procedure.