ee 64 linear system theory
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EE 64EE 64Linear System TheoryLinear System Theory
M. R. Gustafson II
Adjunct Assistant Professor
Duke University
Introduction (Education)Introduction (Education)
BSE in Electrical EngineeringBSE, MS, and PhD in Mechanical
Engineering and Materials ScienceStarting my twelfth year at Duke
Introduction (Military)Introduction (Military)
Duke NROTC 1989-1993Lieutenant, U.S. Naval Reserve
Engineering Duty OfficerNaval Research Laboratories
Science and Technology Unit, Raleigh, NC
Class ObjectivesClass 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.
Resources (Books)Resources (Books)
Signals & Systems, Alan V. Oppenheimer and Alan S. Willsky
Linear System Theory Lecture Notes, Dean McCumber
Resources (Web)Resources (Web)
OIT Guide– http://www.oit.duke.edu– http://www.oit.duke.edu/unix-manual
Class Web page– http://kepler.egr.duke.edu/EE64F00
• Syllabus, grading, assignment information, policies
Resources (Newsgroup)Resources (Newsgroup)
duke.courses.ee64The 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)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 GradingAssignments and Grading
Breakdown:– (15%) Homework– (5%) Correlation Project– (10%) Stabilization Project– (15%) Radio Project– (15%) Test I– (15%) Test II– (25%) Final Exam
HomeworkHomework
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.
ProjectsProjects
Correlation Project– Detect the presence of a sequence in a
noisy signal using correlationRadio Project
– Build a working AM/FM radio and understand its major components
Analysis and Stabilization Project– Model a dynamic system and stabilize it
analytically
Course Web PageCourse 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 NewsgroupCourse Newsgroup
duke.classes.ee64tin program
– Finding groups– Posting messages– Saving messages– Mailing messages
demonstration
SignalsSignals
What is a signal?What is the difference between a
continuous and a discrete signal?– What is "Xeno's Paradox?"
Signal PowerSignal 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:
22 |)(|)(1
)( txtvR
tp
Average Signal PowerAverage Signal Power
Given that definition, the average power of a signal x(t) between times t1 and t2 is:
The average power over all time is:
dttxtt
Pt
tttav
2
121
2
12, |)(|
1
dttxT
PT
TT 2|)(|2
1lim
Signal EnergySignal 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:
dttxEt
ttt 2
121
2|)(|
dttxET
TT 2|)(|lim
Power / Energy SignalsPower / 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
T
EP
Tav 2
lim,
Signal TransformationsSignal 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)
0)()( ttxtxty
Signal PropertiesSignal 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 PartsEven / Odd Parts
The even part of a signal is given by
The odd part of a signal is given by
)()(2
1)()}({ txtxtxtx e
)()(2
1)()}({ txtxtxtx o
Assignment for WednesdayAssignment for Wednesday
Check out the class web pageCheck out the class newsgroup
Read Chapter 1 in Oppenheim & Willsky
Class Feedback SystemClass Feedback System
Four class members to present informal “status report” on how class and lab are going
Volunteers?
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