ECE 235 - Fall 2009

University of California, Santa Barbara
Department of Electrical and Computer Engineering

Stochastic Processes in Engineering

ECE 235 - Fall 2009

Instructor: Prof. U Madhow

Schedule: Tuesdays and Thursdays, 4-5:50 pm, Phelps 1437
Office hours: Mondays 10-noon, Rm 3111, Harold Frank Hall

ANNOUNCEMENTS:

Office hours switched to Mondays 10-noon

WHY THIS COURSE

Probabilistic models and tools are universally employed for design and understanding of both manmade and natural systems. Graduate research in many fields of electrical and computer engineering therefore requires a solid grounding in the mathematical basis for these tools. The goal of this course is to provide a concrete feel for the modeling and computations involved, as well as the kind of theoretical guarantees and approximations we can provide (e.g., convergence, limit theorems, optimal estimation), for stochastic systems.

REQUIRED TEXT

Bruce Hajek, An Exploration of Random Processes for Engineers. Available online at http://www.ifp.uiuc.edu/~hajek/Papers/randomprocesses.html

(The course is mainly based on Chapters 1-4, 7, 8 of the text, but they are not necessarily covered in order, and we may sample some of the other chapters, time permitting.)

RECOMMENDED TEXT

Stark and Woods, Probabillity and random processes with applications to signal processing, Prentice Hall, 2002.

GRADING

Homework: 20%
Probability Quiz: 5%
Midterm Exam: 30%
Final Exam: 45%

HOMEWORK POLICY

Collaboration on homeworks is allowed, but each student must turn in independently written solutions. Copying carries severe penalties. Homework will typically be assigned weekly, on or before Monday, and will be due in the course homework box the following Monday by noon. Late submissions will not be accepted.

EXAMS

Probability quiz: Tuesday, October 13 (the last half hour of class)
Midterm exam: Tuesday, November 3, 4-5:50 pm, in class
Final exam: Friday, December 11, 4-7 pm

TENTATIVE COURSE OUTLINE

(3 lectures)
THE BASICS: Probability, random variables; distribution function; expectation; random vectors; Gaussian random vectors; transformations of random variables and vectors; standard inequalities (Markov, Chebyshev, Jensen)

(4 lectures)
CONVERGENCE AND LIMIT THEOREMS: convergence of sequences of random variables almost surely, in probability, in mean square and in distribution; laws of large numbers; central limit theorem; Chernoff bound and large deviations; martingales

(5 lectures)
INTRODUCTION TO RANDOM PROCESSES: Independent increments processes (Poisson and Wiener); Markov processes; Gaussian random processes; stationary and WSS random processes

(5 lectures)
SECOND ORDER RANDOM PROCESSES: mean square calculus; Karhunen-Loeve expansion; spectral representation; random processes through linear systems; white Gaussian noise

(3 lectures)
INTRODUCTION TO ESTIMATION: orthogonality principle; conditional expectation; linear MMSE estimation

HOMEWORK

Problem Set 1 (due Monday October 5 by noon, in course homework box)
Hajek, Problems 1.1, 1.5, 1.9, 1.11, 1.13, 1.17, 1.19, 1.25, 1.29
Solutions

Problem Set 2 (due October 12)
Revised homework: only Problems 1-4 are to be turned in (i.e., of the book problems, only Problem 3.1 is included)
Solutions

Problem Set 3 (due Monday October 26 by noon in course homework box)
Solutions

Problem Set 4 (due Tuesday, November 3 by noon, in course homework box)
Addendum to Problem Set 4
Solutions

Problem Set 5 (due Tue, Nov 24 in course homework box)
Solutions

Problem Set 6 (due Thu, Dec 3 by noon, in course homework box)
Solutions, part 1
Solutions, part 2

EXAMS

Probability Quiz

Midterm Solutions

Solutions to Final Exam

PROJECTS

HANDOUTS/CLASS NOTES

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