Transcript Course Introduction

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 1989-1993
 Lieutenant, U.S. Naval Reserve
Engineering Duty Officer
 Naval Research Laboratories Science
and Technology Unit, Raleigh, NC

Class Objectives



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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
– 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)
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 W
resistor. Assuming you have a signal
x(t), the power is:
1 2
p(t )  v (t ) | x(t ) |2
R
Average Signal Power
Given that definition, the average
power of a signal x(t) between times
t1 and t2 is:
1 t
2
Pav ,t t 
|
x
(
t
)
|
dt

t2  t1 t
 The average power over all time is:

2
1
2
1
P  lim
T  2T
1

T
T
| x (t ) |2dt
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:
t2
Et1t2   | x(t ) |2dt
t1
The total signal energy is:
T
E  lim  | x(t ) | dt
T  T
2
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

Pav ,
E
 lim
T   2T
Signal Transformations

Given a signal x(t), a signal y(t) can
be written based on x(t) using
scaling and shifting
y(t )  x(t   )  x t  t0 

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
1

{x (t )}  xe (t )  x (t )  x ( t )
2

The odd part of a signal is given by
1

{x (t )}  xo (t )  x (t )  x ( t )
2
Next Time
Complex exponentials
 Unit impulse and step functions
 Systems and system properties
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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??