ECE 352 Systems II

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ECE 352 Systems II

• Manish K. Gupta, PhD
• Office Caldwell Lab 278
• Email guptam_at_ece.osu.edu
• Home Page http//www.ece.osu.edu/guptam
• TA Zengshi Chen Email chen.905_at_osu.edu
• Office Hours for TA in CL 341  TBD
• Home Page http//www.ece.osu.edu/chenz/

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Acknowledgements

• Various graphics used here has been taken from
  public resources instead of redrawing it. Thanks
  to those who have created it.
• Thanks to Brian L. Evans and Mr. Dogu Arifler
  (some of their slides are used here)
• Thanks to Randy Moses and Bradley Clymer

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Course Web Page http//www.ece.osu.edu/guptam/p
ublic_html/home/courses/ece352/index.html
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Tentative Outline

• Frequency Response and Sampling Review 2
  Chapter 5
• Laplace Transforms 6 Chapter 8
• Transfer functions, stability and step
  responses 3 Chapter 9
• Z-Transforms 5 Chapter 11
• Transfer functions, stability and step responses
  (DT) 3 Chapter 11
• State variable descriptions 5 Chapter
  13
• Applications to Communications, Control and
  Signal Processing 4
• selected topics from Chapters 6, 10, and 12
• A more detailed tentative time line is at
• http//www.ece.osu.edu/guptam/public_html/home/co
  urses/ece352/timeline.pdf

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References Other Linear Systems Texts

• Haykin and Van Veen, Signals and Systems, Wiley,
  1999.
• Oppenheim and Willsky, Signals and Systems,
  Prentice-Hall, 1997.
• Lindner, Introduction to Signals and Systems,
  McGraw-Hill, 1999.
• Phillips and Paar, Signals, Systems, and
  Transforms, 2nd ed.,Prentice-Hall, 1999.
• Study Guides
• Hsu, Schaum's Outline of Theory and Problems of
  Signals and Systems, McGraw-Hill, 1995.

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References on Matlab

• The Mathworks, Inc., The Student Edition of
  Matlab, Prentice-Hall.
• Biran and Breiner, Matlab for Engineers
  Addison-Wesley, 1995.
• This is a good elementary introduction to Matlab.
  
• Hanselman and Littlefield, Mastering MATLAB 6 A
  Comprehensive Tutorial and Reference, Prentice
  Hall, 2001.
• This is an excellent reference for both beginners
  and advanced users, with helpful hints on how to
  do many elemenatry and advanced operations in
  Matlab.

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Other Tentative Plans

• Grading The tentative grading schedule is as
  follows
• Midterm 1 25
• Midterm 2  25
• Homework and /Projects 15
• Final 35
• Homework and / OR Projects Homework will be
  assigned regularly in class (Type I II)
• Homework is considered an integral part of this
  course, and you are expected to work all homework
  assignments. Homework will include computer
  assignments that use Matlab. 
• Type I home works you have to submit in time.
  Late homework or projects will receive a grade of
  zero.
• Type II home work (class home work No submission
  ? )
• Attendance You are responsible for all
  assignments, changes of assignments,
  announcements, and other course-related events
  which occur in class.

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• Please Complete First Day Survey and
• Enjoy the class !
• Any Questions ?

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What is Signal ?
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What is System ?
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Audio CD Samples at 44.1 kHz

• Human hearing is from about 20 Hz to 20 kHz
• Sampling theorem (We will cover this later)
  sample analog signal at a rate of more than twice
  the highest frequency in the analog signal
• Apply a filter to pass frequencies up to 20 kHz
  (called a lowpass filter) and reject high
  frequencies, e.g. a coffee filter passes water
  through but not coffee grounds
• Lowpass filter needs 10 of cutoff frequency to
  roll off to zero (filter can reject frequencies
  above 22 kHz)
• Sampling at 44.1 kHz captures analog frequencies
  of up to but not including 22.05 kHz.

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Coverage

• Analysis of linear subsystems within control,
  communication, and signal processing systems
• Examples of electronic control systems?
• Antilock brakes
• Engine control
• Chemical processing plant
• Examples of signal processing systems?

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Signal Processing Systems

• Speech synthesis and speech recognition
• Audio CDs
• Audio compression (MP3, AC3)
• Image compression (JPEG, JPEG 2000)
• Optical character recognition
• Video CDs (MPEG 1)
• DVD, digital cable, and HDTV (MPEG 2)
• Wireless video (MPEG 4/H.263)
• Examples of communication systems?

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Communication Systems

• Voiceband modems (56k)
• Digital subscriber line (DSL) modems
• ISDN 144 kilobits per second (kbps)
• Business/symmetric HDSL and HDSL2
• Home/asymmetric ADSL and VDSL
• Cable modems
• Cell phones
• First generation (1G) AMPS
• Second generation (2G) GSM, IS-95 (CDMA)
• Third generation (3G) cdma2000, WCDMA

Analog
Digital
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Wireline Communications
Internet
DSLAM
Central Office
Customer Premises
ADSL modem
ADSL modem
PSTN
Voice Switch
Lowpass Filter
Lowpass Filter

• HDSL High bitrate 1.544 Mbps in both directions
• ADSL Asymmetric 1-10 Mbps down, 0.5-1 Mbps up
• VDSL Very high bitrate, 22 Mbps down, 3 Mbps up

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Wireless Communications

• Time-frequency (Fourier) analysis
• Digital communication increases SNR/capacity
• Antenna array adds further increase in SNR
  capacity by using spatial diversity
• 2.5G and 3G systems transmit voice data

Picture by Prof. Murat Torlak, UT Dallas
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Networking

• Internet
• Video-on-demand
• Sonet
• Asynchronous Transfer Mode (ATM)
• Broadband Integrated Services Network (ISDN)
• Gigabit Ethernet
• 10 Gigabit Ethernet

Picture by Prof. Jean Walrand, UC Berkeley
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Signals

• Continuous-time signals are functions of a real
  argument
• x(t) where t can take any real value
• x(t) may be 0 for a given range of values of t
• Discrete-time signals are functions of an
  argument that takes values from a discrete set
• xn where n ? ...-3,-2,-1,0,1,2,3...
• We sometimes use index instead of time when
  discussing discrete-time signals
• Values for x may be real or complex

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Analog vs. Digital

• The amplitude of an analog signal can take any
  real or complex value at each time/sample
• Amplitude of a digital signal takes values from a
  discrete set

1
-1
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Systems

• A system is a transformation from one signal
  (called the input) to another signal (called the
  output or the response).
• Continuous-time systems with input signal x and
  output signal y (a.k.a. the response)
• y(t) x(t) x(t-1)
• y(t) x2(t)
• Discrete-time system examples
• yn xn xn-1
• yn x2n

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Linearity

• Linear systems
• Output is linear transformation of input
• Linear transformation T satisfies both
• Homogeneity
• Tk x(t) k Tx(t)
• k is a scalar constant and x(t) is an input
• Additivity
• Tx1(t) x2(t) Tx1(t) Tx2(t)
• x1(t) and x2(t) are two inputs
• x1(t) x2(t) is a superposition (addition) of
  inputs

y(t)
x(t)
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Time-Invariance

• A shift in the input produces a shift in the
  output by the same amount
• If Tx(t) y(t), then Tx(t -t) y(t -t) for
  all real-valued time shifts t
• Is the following system time-invariant?
• y(t) x(t) x(t -1)

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Causality

• Output depends only on the current and past
  inputs and past outputs
• y(t) y(t -1) x(t) 2 x(t -1) is causal
• y(t) y(t 1) x(t 1) - 2 x(t -100) is NOT
  causal
• For systems that involve functions of time (e.g
  audio signals), we must use causal systems if we
  must process signals in real-time
• For systems that involve functions of spatial
  coordinates (images), this is not of concern when
  entire image is available for processing

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• Time domain analysis
• Signals and systems in continuous and discrete
  time
• Convolution finding system response in time
  domain
• Generalized frequency domain analysis
• Laplace and z transforms of signals
• Transfer functions of linear time-invariant
  systems
• Tests for system stability
• Frequency domain analysis
• Fourier series
• Fourier transform of continuous-time signals
• Frequency responses of systems

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???
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Mars Spirit Rover

• Transmits pictures
• At 11 kbits/sec (1/3 telephone modem rate)
• Across 300 million miles (485 million km)
• Using a 140 watt transmitter
• HOW? Image coding (signal processing) and digital
  communications
• Navigation
• Lands within 5 miles after traveling 300 million
  miles
• 3mm error on a trip from Columbus to Cleveland
• 50 minute round-trip communication delay
• HOW? feedback control

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Systems Applications

• Signal processing
• How do I encode images in the fewest bits
  possible, and so that bit errors dont kill image
  quality?
• Communications
• How do I reliability (few bit errors) transmit
  bits over 300 million miles with 140 watts of
  power?
• Control systems
• How do I design feedback systems to provide
  robustness to uncertainties?

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Feedback Control
y(t) actual track
r(t) desired track
Propulsion and steering system
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Feedback Control
y(t) actual track
r(t) desired track
Propulsion and steering system


-
Steering correction system
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ECE352 Goals

• You will learn to work with signals and systems
  in the time and frequency domains.
• You will work with continuous-time and
  discrete-time signals and systems, and know how
  they relate.
• You will learn mathematical techniques to analyze
  and design signals and systems.
• You will learn how to apply these techniques to
  problems in ECE fields.

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y(t)
x(t)
D/A
A/D
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First Day Class Home Work No Submission

• Review ECE 351
• Read Pages 358-363 (Chapter 8)
• Play with Matlab !

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Fourier Transform
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Laplace Transform