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ECE-515

ECE-515: Random Variables and Stochastic Processes
Fall 2009, TR-9:30-10:45, BW-126

Course description:This is a graduate level course on random signals (stochastic processes). It covers the review of probability theory including probability spaces, random variables, probability distributions, density functions, characteristic functions, convergence of random sequences, and laws of large numbers. Fundamental concepts of random processes including stationary, ergodicity, autocorrelation function, power spectral density, and transmission of random processes through linear systems is covered as well. Finally, we will study special random processes such as Gaussian and Poisson processes with applications to electrical and computer engineering at a fairly rigorous level.

References:

• A. Papoulis, Probability, Random Variables, and Stochastic Processes, McGraw-Hill, 2003, ISBN 0-07-366011-6.
• Course notes

Content:

• Probability Theory
• Repeated Trials
• Random Variable
• Functions of one Random Variable
• Two Random Variables and Random Vectors
• Moments and Conditional Distributions
• Sequences of Random Variables
• Stochastic Processes
• Spectral Representation
• Ergodicity
• Entropy

Grading Scheme:
Students’ performance is evaluated with homework, a midterm, and a final exam.

Homework   15%
Midterm       35%
Final exam   50%

If the student fails in both midterm and final projectthe homework will count for 0%.

Prerequisite: To follow the course, in addition to basic notions of probability, the student is expected to have some familiarity with the basic notions of sets, sequences, convergence, linear algebra, and Fourier transforms. The formal pre-requisites are:

• MAT 332 or equivalent

Disability statement:

Students with disabilities who may need services or accommodations to fully participate in this class should contact Ann Smith, Director of Disability Services in 121 East Annex, (voice) 581-2319, (TTY) 581-2325 as early as possible in the semester.

Instructional Contingency Plan:

In the event of disruption of normal classroom activities due to an H1N1 swine Flu outbreak, the format for this course may be modified to enable completion of the course. In that event, you will be provided an addendum to this syllabus that will supersede this version.