An adaptive optimal-kernel time-frequency representation
Jones, D.L.; Baraniuk, R.G.
Signal Processing, IEEE Transactions on
Volume 43, Issue 10, Oct 1995 Page(s):2361 - 2371
Digital Object Identifier 10.1109/78.469854
Summary: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 in the present paper, based on a signal-dependent radially
Gaussian kernel that adapts over time, surmounts these difficulties. 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
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