CATALOG DESCRIPTION: Advanced topics in random processes: point processes, Wiener processes; Markov processes, spectral representation, series expansion of random processes, linear filtering, Wiener and Kalman filters, optimum receivers and matched filters.
REQUIRED TEXT: Leon-Garcia, Probability and Random Processes for Electrical Engineering , Prentice Hall, 2 nd edition (1994)
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.
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.