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Signal Detection Theory deals with the problem of deciding from noisy
observations which of a set of (deterministic or random) signals is
present. As a statistics problem, this is quite straightforward: under
a variety of criteria, the optimum decision rule is to compare
"likelihood ratios" against suitable thresholds. However from an
engineering point of view, the problem is just beginning. The issue is
not so much numerical computation of the LR, but what to do with
poorly specified models, how much to make intelligent approximations
and simplifications, hardware implementations, etc. So engineers (and
statisticians) study a variety of specific problems in order to obtain
"structural information" on the form of the likelihood ratio.
We shall illustrate this process and show how fairly advanced tools from martingale theory help in this effort. Among other results, we shall encounter the important role of mean-square-error estimation in the detection problem, and surprising parallels between detection problems for random signals with "additive" Gaussian noise and with "multiplicative" Poisson-type noise. |
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Dr. Thomas Kailath is the Hitachi America Professor of Egineering,
in the Department of Electrical Engineering, Stanford University.
He is a member of the National Academy of
Science, as well as the National Academy of
Engineering. Prof. Kailath is a Fellow of the IEEE and the
Institute of Mathematical Statistics. He is also a Past President
of the IEEE Information Theory Group.
Dr. Kailath is a Co-founder, Member and ex-Chairman of the Board of Directors, Integrated Systems, Inc., which is now a publicly held company. He has received numerous best paper awards. His research intrests include Information Theory, Communication, Computation, Control, Linear Systems, Statistical Signal Processing and VLSI systems. |