**Description:** An introduction to stochastic processes and probabilistic
modeling with emphasis on communication system applications.

**Prerequisites:** Introductory probability and linear
systems, or consent of instructor.

**
Textbooks:** A. Papoulis and S. U. Pillai,

**Course Website:**

Public access:
http://www.comm.utoronto.ca/~liang/courses/ECE1500FA09/

Login required: ECE1500 course website on Blackboard through the UofT Portal

**Instructor:** Ben Liang

Office: Bahen Centre Room 4122 (through doors 4113 or 4145)

Contact:
http://www.comm.utoronto.ca/~liang

**TA:** Hossein Seyedmehdi, BA4000, hossein@comm.utor...

**Lectures:**

Tuesdays 4 - 6 pm, BA1210

Thursdays 2 - 3 pm, BA1240

**Office Hours: **

Thursdays 3 - 4 pm, BA4122

**Grading Policy:** There will be bi-weekly homework
assignments, one midterm exam, and one final exam. The weights for different grading components:

Homework 10%

Midterm Exam 40%

Final Exam 50%

The homework assignments can be found
here. Homework will be graded solely on the basis of effort, not
correctness. Solution to the homework problems will be available on the
Blackboard course website when they are due, usually two weeks after they are
assigned.

**
Topical Outline: **(A

- Probability Theory Overview - axioms of probability,
repeated trials, conditional probability, random variables, characteristic
functions (
*2 weeks*) - Sequence of Random Variables - joint statistics, conditional
statistics, stochastic convergence, law of large numbers, central
limit theorem (
*1 week*) - Stochastic Processes - definitions and interpretations,
classical examples, statistics, stationarity, ergodicity, system
with stochastic inputs, power spectrum, Fourier series and Karhunen-Loève
expansion (
*3.5 weeks*) - Mean Square Estimation - orthogonality principle, linear
mean square estimation, geometric interpretation, Wiener filtering (
*1 week*) - Discrete-Time Markov Chain - classification, Chapman-Kolmogorov
equations, stationary distribution, limiting distribution, absorption
probabilities, mean absorption time, branching (
*2 weeks*) - Continuous-Time Markov Chain - sojourn time, transition rates,
birth-death processes, Markovian queues, time reversibility (
*1.5 weeks*)