Syllabus

ECE528: Introduction to Random Processes in ECE Spring 2017

Instructor: Zhi “Gerry” Tian <ztian1@gmu.edu>

Teaching Assistant: Massieh Kordi Boroujeny <mkordibo@masonlive.gmu.edu>

Class Meetings: Lectures (CRN 11125) – Tues. 4:30pm-7:10pm, Planetary Hall 122

Recitation (CRN 11243) – Wed. 7:20pm-8:35pm, Krug Hall 253

Office Hours: Tuesdays 2-4pm, Thursdays 3:00-4:30pm; @ Nguyen Engineering Building Room 3242

Course website: http://blackboard.gmu.edu

• Notes, home assignments and other course materials will be posted on Blackboard • Class announcements such as schedule changes and problem discussions will be posted via Blackboard.

Each student is responsible for keeping up with the posted announcements.

Textbook: Introduction to Probability, Second Ed. by Dimitri P. Bertsekas and John N. Tsitsiklis, Athena Scientific, 2008. ISBN 978-886529-23-6

Supplemental books:

Probability, Statistics, and Random Processes, 3rd Edition by Alberto Leon-Garcia, Pearson Prentice Hall, 2008.

Probability, Random Variables, and Stochastic Processes, 3rd Edition by Athanasios Papoulis, McGraw-Hill Inc, 1991.

Prerequisites: ECE 220 and STAT 346, or permission of instructor. Ability to think clearly and formulate simple mathematical proofs is essential. Be ready to pick up some basic MATLAB skills.

Course Description: This course develops the mathematical theory of probability, random variables and random processes for Electrical Engineers. The goal is to teach the basic theoretical concepts and techniques for solving problems that arise in practice, with focus on statistical techniques as applied to the study of random signals and noise. Beginning with the Axioms of Probability, this course introduces the assignment of probability laws to discrete and continuous sample spaces, which leads to the concept of random variables, pairs of random variables and finally random processes. Topics include random variables and their functions; random processes in continuous and discrete time and space; stationarity and ergodicity vectors; expectation and variance; conditional expectation; moment-generating and characteristic functions; random processes such as white noise and Gaussian; second-order properties of random processes such as autocorrelation and power spectral density; interaction of random processes with linear systems; linear filtering of random processes; and basic ideas of estimation and detection. These concepts and techniques prepare students for advanced study of topics in electrical and computer engineering, such as communication theory, signal and image processing, remote sensing, control theory, discrete-event systems, and computer networks.

Requirements: Weekly homework assignments, quizzes, in-class midterm exams*, and final exam.

Attendance is expected. Students are responsible for all assigned readings, class lectures, as well as material covered in class that is not in the book.

Homework Assignments: All homework assignments are due in class on the specified due date, with no late assignments accepted.

Grading Policy: homework and quizzes – 20%; mid-term – 35%; final exam – 45%.

Course Outline and Schedule (subject to change)

1. Review of Probability: 1.1. Set Theory, Probability Spaces; 1.3 Conditional Probability and Independence

2. Random Variables: 2.1 Basic Concepts; 2.2 Distribution, Density, and Mass Functions; 2.3 Functions of Random Variables; 2.4 Expectations, Moments, and Characteristic Functions

3. Pairs of Random Variables: 3.1 Joint and Marginal Distributions; 3.2 Conditional Distributions and Independence; 3.3 Functions of Two Random Variables; 3.4 Expectations and Correlations

4. Random Vectors: 4.1 Joint, Marginal, and Conditional Distributions; 4.2 Functions of Several Random Variables; Expectations and Correlations; 4.3 The Multivariate Gaussian Distribution

*** MIDTERM EXAM (March 7) *** Spring break: March 13-19 ***

5. Sequences of Random Variables; Convergence Concepts; Law of Large Numbers and Central Limit Theorem

6. Stochastic Processes 6.1. Basic Concepts 6.2. Covariance, Correlation, and Stationarity 6.3. Gaussian Processes and Brownian Motion 6.4. Poisson and Related Processes 6.5. Power Spectral Density 6.6. Stochastic Processes and Linear Systems

7. Introduction to Markov Chains 7.1. Markov Processes 7.2. Markov Chains

*** FINAL EXAM (Tuesday, May 16, 4:30pm – 7:15pm) ***

Course and University Policies

• Honesty and Integrity: Mason expects students to pursue their academic work with honesty and integrity. Students should feel free to work in groups to discuss lecture material and homework assignments; however, under no circumstance should a student represent another’s work as his or her own. Copying solutions for assigned homework problems, from any source, constitutes a violation of the university honor code. Any forms of cheating may cause penalties, from getting F in this course to academic actions in accordance with university policy.

• Email Communications: Students must use their MasonLive email account to receive important University information, including messages related to this class. See http://masonlive.gmu.edu for more information. Homework assignments and other course material will be emailed to your MasonLive email account. Also, when you send me an email, please write ece528 on the subject line.

• University Policies: The University Catalog, http://catalog.gmu.edu, is the central resource for university policies affecting student, faculty, and staff conduct in university academic affairs. Other policies are available at http://universitypolicy.gmu.edu/. All members of the university community are responsible for knowing and following established policies. Academic integrity is of great importance to the Mason community. Mason provides accommodations through the Office of Disability Services.