ECE 331: Introduction to Random Signal Analysis and Statistics

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ECE 331 - Introduction to Random Signal Analysis and Statistics

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ECE 331: Introduction to Random Signal Analysis and Statistics, Spring 2007 (Gubner)

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Catalog Description

331 Introduction to Random Signal Analysis and Statistics. I, II; 3 cr. Introduction to probability, random variables, and random processes. Confidence intervals, introduction to experimental design and hypothesis testing. Statistical averages, correlation, and spectral analysis for wide sense stationary processes. Random signals and noise in linear systems. P: ECE 330.

Course Prerequisite(s)

ECE 330

Prerequisite knowledge and/or skills

Spectral characterizations of signals via Fourier & Laplace transform techniques
Input/Output descriptions of linear systems via Laplace transform techniques

Textbook(s) and/or other required material

A. Leon-Garcia, Probability and Random Processes for Electrical Engineering, 2nd ed., Addison-Wesley, 1993.
R. D. Yates and D. J. Goodman, Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers, 2nd ed., Wiley, 2004.
J. A. Gubner, Probability and Random Processes for Electrical and Computer Engineers, Cambridge, 2006.

Course objectives

This course provides the student with an operational understanding of random variables, random vectors, and random processes. Special emphasis is given to continuous-time, second-order random processes, including correlation functions and power spectral densities. The effect of passing such processes through linear time-invariant systems is also analyzed. Confidence intervals and reliability. The course concludes with an introduction to discrete-time Markov chains.

Topics covered

Discrete and continuous random variables, probability mass functions and densities, independent random variables, expectation, Chebyshev's inequality and the weak law of large numbers.
Cumulative distributions, mixed random variables, transformations of random variables, reliability.
Conditional probability and expectation, the law of total probability.
Continuous-time, second-order random processes, correlation functions, power spectral densities, random processes filtered through linear time-invariant systems.
Parameter estimation and confidence intervals.
Discrete-time Markov chains.

Class/laboratory schedule

VARIES WITH SEMESTER OF OFFERING: Three 50 minute lectures per week OR two 75 minute lectures per week.

Contribution of course to meeting the professional component

This course contributes primarily to the students' knowledge of engineering topics, but does not provide design experience.

The following statement indicates which of the following considerations are included in this course: economic, environmental, ethical, political, societal, health and safety, manufacturability, sustainability.

economic manufacturability sustainability

Relationship of course to undergraduate degree program objectives and outcomes

This course primarily serves students in the department. The information below describes how the course contributes to the undergraduate program objectives.

knowledge in the basic techniques of mathematics and the physical sciences knowledge of measurement techniques and experimental procedures in core electrical and computer engineering applications

Assessment of student progress toward course objectives

Homework 15%; Mid-term 1 25%; Mid-term 2 25%; Final Exam 35%

Person(s) who prepared this description

John A. Gubner

Copyright 2009 The Board of Regents of the University of Wisconsin System
Date last modified: 21-Jul-2009
Content by: ece@engr.wisc.edu
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