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.