ECEN 5652  Detection and Extraction of Signals from Noise
Catalog Data 
ECEN 5652 (3). Detection and Extraction of Signals from Noise.
Introduces detection,
estimation and time seriesanalysis. Topics include hypothesis testing,
detection of known form and random signals, least squares parameter
estimation, maximum likelihood theory, minimum meansquared error
estimation, KalmanWiener filtering, prediction in stationary time
series, and modal analysis. Applications include studies
in communications, control, and experimental modeling.

Credits and Design 
3 credit hours. Elective course.

Prerequisite(s) 
ECEN 5612, Noise and Random Processes

Textbook 
Statistical Signal Processing, L. Scharf, 1991.
References:
 An Introduction to Detection and Estimation,
V.H. Poor, SpringerVerlag, 1989.
 Detection, Estimation and Modulation Theory,
H.L. VanTrees, Wiley, 1968.
 Principles of Communication Engineering,
Wozencraft and Jacobs, Wiley, 1965.

 
Course Objectives 
Understanding of the fundamentals of
hypothesis testing and estimation and their engineering applications in
various signal detection and extraction problems.

Topics Covered 
 Review of applied probability
and random processes, the KarhunenLoeve expansion. Statistical modeling
and an introduction to detection and estimation problems.
 Fundamentals
of linear algebra: vector spaces, linear independence,
QR factorizations, linear subspaces, singular value decompositions,
projections, rotations, psuedoinverses.
 Detection theory: simple
hypothesis testing under the Bayes' criterion and the NeymannPearson
criterion; sufficient statistics. Composite hypothesis testing, the
NeymannPearson criterion and the notion of invariance. The generalized
likelihood ratio test and its optimality. Minimax detection
and sequential detection. Applications include detection problems
in communications and radar/sonar signal processing including the
linear statistical model and the multivariate Gaussian
model.
 Estimation theory: maximum likelihood estimation and
sufficiency, CramerRao inequality, Bayesian and minimax parameter
estimation including minimum meansquared error and maximum a posteriori
estimation, linear minimum meansquared estimation; applications
including the multivariate normal model, linear statistical model, Kalman
and Wiener filtering.

Last revised: 080211, PM, ARP.