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ECE-515

ECE-515: Random Variables and Stochastic Processes

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.

Prerequisite:

• MAT 332 or equivalent

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%.

Academic honesty
Academic dishonesty includes cheating, plagiarism, and all forms of misrepresentation in academic work, and it is unacceptable at the University of Maine. As stated in the University of Maine’s online undergraduate “Student Handbook,” plagiarism (the submission of another’s work without appropriate attribution) and cheating are violations of the University of Maine Student Conduct Code. An instructor who has probable cause or reason to believe a student has cheated may act upon such evidence, and will report the case to the supervising faculty member or the Department Chair for appropriate action.

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 emergency situation of viral outbreak such as H1N1 swine flu, 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. The main change in format will involve online collaboration and teaching tools replacing the classroom activities.