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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 mean-squared error estimation, Kalman-Wiener 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.


  1. An Introduction to Detection and Estimation, V.H. Poor, Springer-Verlag, 1989.
  2. Detection, Estimation and Modulation Theory, H.L. VanTrees, Wiley, 1968.
  3. 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
  1. Review of applied probability and random processes, the Karhunen-Loeve expansion. Statistical modeling and an introduction to detection and estimation problems.
  2. Fundamentals of linear algebra: vector spaces, linear independence, QR factorizations, linear subspaces, singular value decompositions, projections, rotations, psuedoinverses.
  3. Detection theory: simple hypothesis testing under the Bayes' criterion and the Neymann-Pearson criterion; sufficient statistics. Composite hypothesis testing, the Neymann-Pearson 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.
  4. Estimation theory: maximum likelihood estimation and sufficiency, Cramer-Rao inequality, Bayesian and minimax parameter estimation including minimum mean-squared error and maximum a posteriori estimation, linear minimum mean-squared estimation; applications including the multivariate normal model, linear statistical model, Kalman and Wiener filtering.

Last revised: 08-02-11, PM, ARP.