REQUIRED TEXT: Leon-Garcia, Probability and Random Processes for Electrical Engineering , Prentice Hall, 2 nd edition (1994)

REFERENCE TEXTS:

A. Papoulis, Probability, Random Variables and Stochastic Processes , Boston McGraw Hill, 4 th edition

Stark and Woods, Probability, Random Processes, and Estimation Theory for Engineers , Prentice Hall, 2 nd edition (1994)

Wozencraft and Jacobs, Principles of Communication Engineering , Wiley

Brown and Hwang, Introduction to Random Signals and Applied Kalman Filtering , Wiley, 2 nd edition

Gardner , Introduction to Random Processes , McGraw Hill, 2 nd edition

Van Trees, Detection, Estimation, and Modulation Theory, Part I , Wiley

B. Picinbono, Random Signals and Systems , Prentice Hall (1993)

COURSE DIRECTOR: Abraham Haddad

COURSE GOALS: To provide entering graduate students with a broad coverage of the use of random processes in communications, control, and signal processing.

PREREQUISITES BY COURSES: EECS 422

PREREQUISITES BY TOPIC:

1. Random processes.

2. Fourier transforms

DETAILED COURSE TOPICS:

Week 1: Review of independent increment processes.

Week 2: Brownian motion and the Wiener process, Ito integral.

Week 3: Point processes, Poisson processes, Spectral representation.

Week 4: Series expansion of random processes.

Week 5: Linear systems with random inputs (including state space).

Week 6: Linear estimation and orthogonality principle.

Week 7: Wiener filters.

Week 8: Kalman filters.

Week 9: Optimum receivers, matched filters and signal detection.

Week 10: Nonlinear systems with white noise input, phase lock loop.

COMPUTER USAGE: Optional.

LABORATORY PROJECTS: None.

GRADES:

Homeworks – 30%

Midterm exam – 30%

Final exam – 40%

COURSE OBJECTIVES: When a student completes this course, s/he should be able to:

•  Understand the basic types and structures of linear filters and optimum receivers.

•  Understand the use of independent increment processes in linear and nonlinear systems.

•  Understand the basic approaches to the representation of random signals.

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