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Course Syllabus
ECE 450 - Probabilistic Systems in Electrical Engineering - Design and Analysis
Department:
Course Number:
Course Title:
Credit Hours:
Design Credits:
Electrical and Computer Engineering
ECE 450
Probabilistic Systems in Electrical Engineering - Design and Analysis
3.0
0.5
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.
Pre-requisites by Topic
1. Calculus
2. Linear Systems Theory (including Fourier Transforms)
Text, References, and Software
Probabilistic Methods of Signal and System Analysis, Third Edition, Cooper and McGillem, Oxford University Press, 1999.
ISBN 0-19-512354-9.
Software: MATLAB
Learning Outcomes for the Course - After completing this course a student 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.
classify random processes as continuous, discrete or mixed, as deterministic or non-deterministic, 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;
5.
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.
Topics Covered / Course Outline
1.
Basic probability theory with engineering applications
2.
Random variables, moments, probability density functions, distribution functions, characteristic functions, and
transformation of a random variable
3.
Random vectors, mean vectors, correlation matrices, and covariance matrices
4.
Random processes, with emphasis on wide-sense stationary processes, correlation functions, and power spectra
5.
Homework Reviews and Exam
Contribution to Professional Component
Engineering Science
Engineering Design
Math & Basic Sciences
1.0
0.5
1.5
Relationship to Program Outcomes
This course supports the achievement of the following outcomes:
(a)
an ability to apply knowledge of mathematics, science, and engineering to the analysis of electrical 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;
(e)
an ability to identify, formulate, and solve electrical engineering problems;
(k)
an ability to use modern engineering techniques for analysis and design;
(l)
knowledge of fundamental electrical engineering topics including probability and statistics;
(m)
an ability to analyze and design complex devices and systems containing hardware and software components; and
(n)
knowledge of math including differential equations, linear algebra, complex variables and discrete math.