EE 64 Linear System Theory M. R. Gustafson II Adjunct Assistant Professor Duke University

Introduction (Education) BSE in Electrical Engineering BSE, MS, and PhD in Mechanical Engineering and Materials Science Starting my twelfth year at Duke

Introduction (Military) Duke NROTC Lieutenant, U.S. Naval Reserve Engineering Duty Officer Naval Research Laboratories Science and Technology Unit, Raleigh, NC

Class Objectives To learn the fundamental engineering mathematics of signal representations, linear system responses, convolution, and correlation, To understand Fourier series, Fourier transforms, transfer functions, Laplace transforms, state variables, transfer functions, and stability, To see discrete-time signals, z transforms, discrete-time Fourier transforms, and the fast Fourier transform, and To meet other people in engineering.

Introductions & Roll Call

Resources (Books) Signals & Systems, Alan V. Oppenheimer and Alan S. Willsky Linear System Theory Lecture Notes, Dean McCumber

Resources (Web) OIT Guide – – Class Web page – Syllabus, grading, assignment information, policies

Resources (Newsgroup) duke.courses.ee64 The newsgroup will be used to post announcements and answer questions. Use this to post items that are of interest to the rest of the class. Students are allowed to answer questions as long as the answers are correct and do not violate the honor code!

Resources (Public Clusters) MAPLE, MATLAB, and SIMULINK will run on all acpub machines. They will also run over xwin32 and eXodus. Public UNIX machines are in Teer (new!), Hudson Hall, Soc-Psych, Bio-Sci, Carr, West Duke, and Trent. Check the OIT schedule to make sure there is no lab before entering - respect other people's lab times.

Assignments and Grading Breakdown: –(15%) Homework –(5%) Correlation Project –(10%) Stabilization Project –(15%) Radio Project –(15%) Test I –(15%) Test II –(25%) Final Exam

Homework Homework will be assigned each week and turned in the following week. Homework will consist of problems from the texts as well as some problems written up by the instructor.

Projects Correlation Project –Detect the presence of a sequence in a noisy signal using correlation Radio Project –Build a working AM/FM radio and understand its major components Analysis and Stabilization Project –Model a dynamic system and stabilize it analytically

Tests There will be three tests in this class -- two during the semester and one final exam.

Course Web Page kepler.egr.duke.edu/EE64F00 Netscape on acpub –Web crawlers Yahoo Hotbot Google –Unregulated information! Even less trustworthy than regular press :) demonstration

Course Newsgroup duke.classes.ee64 tin program –Finding groups –Posting messages –Saving messages –Mailing messages demonstration

Signals What is a signal? What is the difference between a continuous and a discrete signal? –What is "Xeno's Paradox?"

Signal Power Signal power is calculated assuming that the signal is a voltage on a 1  resistor. Assuming you have a signal x(t), the power is:

Average Signal Power Given that definition, the average power of a signal x(t) between times t 1 and t 2 is: The average power over all time is:

Signal Energy Signal energy is found by recalling that power is the rate of change of energy. Energy, therefore, is the integral of power, so: The total signal energy is:

Power / Energy Signals A power signal is a signal that has infinite total energy An energy signal is a signal that has finite total energy and thus zero average power

Signal Transformations Given a signal x(t), a signal y(t) can be written based on x(t) using scaling and shifting See scale_shift.mws for examples (all programs from class are in ~mrg/public/EE64F00)

Signal Properties A signal x(t) is periodic with period T if it has the property that there is some positive T for which x(t)=x(t+T) A signal x(t) is even if x(t)=x(-t) A signal x(t) is odd if x(t)=-x(-t)

Even / Odd Parts The even part of a signal is given by The odd part of a signal is given by

Next Time Complex exponentials Unit impulse and step functions Systems and system properties

Assignment for Wednesday Check out the class web page Check out the class newsgroup Read Chapter 1 in Oppenheim & Willsky

Class Feedback System Four class members to present informal “status report” on how class and lab are going Volunteers?

Questions?? ?