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ECEN 5652 - Detection and Extraction of Signals from Noise

3 credit hours

Catalog Description: 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.

Prerequisite ECEN 5612, Noise and Random Processes

Textbook: Statistical Signal Processing, L. Scharf, 1991.

Reference: An Introduction to Detection and Estimation, V.H. Poor, Springer-Verlag, 1989. Detection, Estimation and Modulation Theory, H.L. VanTrees, Wiley, 1968. Principles of Communication Engineering, Wozencraft and Jacobs, Wiley, 1965.

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

Topics:

  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.
Computer Usage:
  1. Moderate.
Laboratory Projects:
  1. None.
ABET Category Content:
  • Engineering Science: 1.5 credits or 50%
  • Engineering Design: 1.5 credits or 50%