Course Syllabus
ECE450 – Probabilistic Systems in Electrical Engineering
Department of Electrical & Computer Engineering
1. Course Number and Name:
2. Credit Units/Contact Hours:
3. Course Coordinator:
ECE450 – Probabilistic Systems in Electrical
Engineering
3/3
Debbie van Alphen
4. Text, References & Software
Recommended Text:
Probabilistic Methods of Signal & System Analysis, 3rd edition, G. Cooper, C. McGillem, Oxford
Publishing, 1999
Additional References:
Probability and Random Processes for electrical engineering, A. Leon-Garcia
Software:
MATLAB
Internet Resources:
http//hpme12.me.edu/matlab/html/
5. Specific Course Information
a. Course Description
Develops and demonstrates techniques and models useful for solving a wide range of problems
associated with the design and analysis of various probabilistic systems in electrical engineering
applications. These include radar, communication systems, sonar, control systems, information
theory, computer systems, circuit design, measurement theory, vulnerability analysis, and
propagation.
b. Prerequisite by Topic
Students taking this course are expected to have taken the math courses required of engineers
(calculus and differential equations). In addition familiarity with the following topics are
expected:
Elementary set theory, Boolean algebra and switching circuits (ECE320)
Elementary signal and system theory, Fourier and Laplace transforms, convolutions and transfer
functions (ECE350)
Basic MATLAB skills, including working with vectors/matrices and plotting elementary math
functions (ECE 350)
c. Required Course
6. Specific Goals for the Course
a. Specific Outcomes of Instructions – After completing this course the students should be able to:
1. apply the fundamentals of combinatorics (including combinations and permutations) to
answer basic counting questions;
2. apply the basic axioms and corollaries of probability, conditional probability, Bayes’ Rule,
and the Total Probability Theorem to calculate probabilities of interest for engineering
applications;
3. apply random variable theory (including knowledge of probability densities and cumulative
distribution functions) to determine probabilities, moments, and the effects of
operations/systems on random variables (e.g., Gaussian, Rayleigh, Exponential, Uniform,
Poisson, Bernoulli, and Log-Normal) and random vectors of interest to electrical engineers;
4. Use MATLAB to conduct computer simulations related to electrical engineering problems;
5. classify random processes as continuous, discrete or mixed, as deterministic or nondeterministic, as strict-sense stationary, wide-sense stationary or non-stationary, and as
ergodic or non-ergodic, and to draw sample functions for a given random process; and
6. apply random process theory (including knowledge of correlation functions and power spectral
densities) to evaluate moments of a random process and to determine the effects of
operations/systems on random processes.
b. Relationship to Student Outcomes
This supports the achievement of the following student outcomes:
a. An ability to apply knowledge of math, science, and engineering to the analysis of electrical
and computer engineering problems.
b. An ability to design and conduct scientific and engineering experiments, as well as to analyze
and interpret data.
c. An ability to design systems which include hardware and/or software components within
realistic constraints such as cost, manufacturability, safety and environmental concerns.
e. An ability to identify, formulate, and solve electrical and computer engineering problems.
k. An ability to use modern engineering techniques for analysis and design.
l. Knowledge of probability and statistics.
n. Knowledge of math including differential equations, linear algebra, complex variables and
discrete math.
7. Topics Covered/Course Outline
1. Introduction to Probability
2. Combinatorics
3. Random Variables, probability density and distribution functions.
4. Expected value, higher moments& characteristic function.
5. Functions of Single Random Variable
6. Generation of arbitrary random variables using computer techniques
7. Several Random Variables, correlation and covariance
8. Functions of Several Random Variables
9. Random Vectors
10. Introduction to Random Processes
Prepared by:
Debbie van Alphen, Professor of Electrical and Computer Engineering, October 2011
Ali Amini, Professor of Electrical and Computer Engineering, March 2013