EE 64 Linear System Theory

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EE 64Linear System Theory

• M. R. Gustafson II
• Adjunct Assistant Professor
• Duke University

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Introduction (Education)

• BSE in Electrical Engineering
• BSE, MS, and PhD in Mechanical Engineering and
  Materials Science
• Starting my twelfth year at Duke

3
Introduction (Military)

• Duke NROTC 1989-1993
• Lieutenant, U.S. Naval ReserveEngineering Duty
  Officer
• Naval Research Laboratories Science and
  Technology Unit, Raleigh, NC

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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.

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Introductions Roll Call
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Resources (Books)

• Signals Systems, Alan V. Oppenheimer and Alan
  S. Willsky
• Linear System Theory Lecture Notes, Dean McCumber

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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

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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!

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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.

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Assignments and Grading

• Breakdown
• (15) Homework
• (5) Correlation Project
• (10) Stabilization Project
• (15) Radio Project
• (15) Test I
• (15) Test II
• (25) Final Exam

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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.

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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

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Tests

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

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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

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Course Newsgroup

• duke.classes.ee64
• tin program
• Finding groups
• Posting messages
• Saving messages
• Mailing messages
• demonstration

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Signals

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

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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

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Average 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

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Signal Energy

• Signal energy is found by recalling that power is
  the rate of change of energy. Energy, therefore,
  is the integral of power, soThe total signal
  energy is

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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

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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)

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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(tT)
• A signal x(t) is even if x(t)x(-t)
• A signal x(t) is odd if x(t)-x(-t)

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Even / Odd Parts

• The even part of a signal is given by
• The odd part of a signal is given by

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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

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Class Feedback System

• Four class members to present informal status
  report on how class and lab are going
• Volunteers?

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Questions??

• ?