Syllabus

ECE528: Introduction to Random Processes in ECE

Spring 2016

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

Teaching Assistant: Venkata S. Veeramachaneni <vveeram2@masonlive.gmu.edu>

Class Meetings: Lectures (CRN 11333) -- W 7:20pm-10:00pm, Music Theater Building (MTB) 1004

Recitation (CRN 11485) -- M 5:55pm-7:10pm, Robinson Hall (R) B102

Office Hours: Wednesdays 4-6pm, Mondays 3:00-4:30pm; @ Nguyen Engineering Building Room 3242

TA Office Hours: Mondays 7-8pm; and Fridays 4-5pm @ENGR 3204

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 1 – 15%; mid-term 2 – 30%; final exam – 35%. * When mid-term 1 is cancelled, the grading is: homework and quizzes – 20%; mid-term – 35%; final exam – 45%.

Course Outline and Schedule (subject to change)

1. Review of Probability: 1.1. Set Thory, 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

*** MIDTERM EXAM 1 (Feb. 17 or 24) – Cancelled ***

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

5. Sequences of Random Variables; Convergence Concepts;

Law of Large Numbers and Central Limit Theorem

***REVIEW *** MIDTERM EXAM 2 (March 23) ***

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 (early May) ***

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.