ECE 352 Systems II

Manish K. Gupta, PhD Office: Caldwell Lab 278

Email: guptam@ece.osu.edu Home Page: http://www.ece.osu.edu/~guptam TA: Zengshi Chen Email: chen.905@osu.edu

Office Hours for TA : in CL 341:  TBD Home Page: http://www.ece.osu.edu/~chenz/

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

Course Web Page: http://www.ece.osu.edu/~guptam/

public_html/home/courses/ece352/index.html

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/courses/ece352/timeline.pdf

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.

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.

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.

• Please Complete First Day Survey and

Enjoy the class !

Any Questions ?

What is Signal ?

What is System ?

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.

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?

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?

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

Wireline Communications

• 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

Customer Premisesdownstream

upstreamVoice

Switch

Central Office

DSLAM

ADSL modem

ADSL modem

Lowpass Filter

Lowpass Filter

PSTN

Internet

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

Picture by Prof. Jean Walrand, UC Berkeley

Networking• Internet• Video-on-demand• Sonet• Asynchronous Transfer

Mode (ATM)• Broadband Integrated

Services Network (ISDN)• Gigabit Ethernet• 10 Gigabit Ethernet

Signals• Continuous-time signals are functions of a real

argumentx(t) where t can take any real valuex(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 setx[n] 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

1

-1

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

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 examplesy[n] = x[n] + x[n-1]y[n] = x2[n]

x(t) y(t)

x[n] y[n]

Linearity• Linear systems

– Output is linear transformation of input

• Linear transformation T{·} satisfies both– Homogeneity

• T[k x(t)] = k T[x(t)]• k is a scalar constant and x(t) is an input

– Additivity• T[x1(t) + x2(t)] = T[x1(t)] + T[x2(t)]• x1(t) and x2(t) are two inputs• x1(t) + x2(t) is a superposition (addition) of inputs

{ }•Tx(t) y(t)

Time-Invariance• A shift in the input produces a shift in the

output by the same amount– If T[x(t)] = y(t), then T[x(t -)] = y(t -) for all real-

valued time shifts • Is the following system time-invariant?

y(t) = x(t) + x(t -1)

Causality• Output depends only on the current and past

inputs and past outputsy(t) = y(t -1) + x(t) + 2 x(t -1) is causaly(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

• 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

???

ECE 352

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

ECE 352

Systems Applications

• Signal processing: – How do I encode images in the fewest bits possible,

and so that bit errors don’t 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?

ECE 352

Feedback Control

Propulsion and steering system

r(t)desired track

y(t)actual track

ECE 352

Feedback Control

Propulsion and steering system

r(t)desired track

y(t)actual track

Steeringcorrection

system

++-

ECE 352

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.

ECE 352

x(t) y(t)CT System

x[n] y[n]DT System

x(t)A/D

y(t)D/A

ECE 352 First Day Class Home Work No Submission

1. Review ECE 351

2. Read Pages 358-363 (Chapter 8)

3. Play with Matlab !

ECE 352

Fourier Transform

ECE 352

Laplace Transform