EE 221Signals Analysis and Systems
Instructor: Dr. Ghazi Al SukkarDept. of Electrical EngineeringThe University of JordanEmail: [email protected]
1Fall 2014
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Course Details
Objective Establish a background in Signal and System Analysis Get familiar with signals and systems applications
Grading First Exam 20% Second Exam 30% Final Exam 50%
Text Book Signals, Systems and Transforms, Prentice Hall, 4th Edition Charles L. Philips et.al
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Useful References
Signals and Systems Analysis, second edition, By: Samir Soliman, et. al Introduction to Comm. Systems, third edition, By: Ferril Stremler Linear Systems and Signals, B.P second edition, By: Lathi
Course Websitehttp://academic.ju.edu.jo/ghazi.alsukkar/default.aspx
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Outline
IntroductionSignals, Systems and Transforms:
• Signal Definition• System definition• Continuous-time vs. Discrete-time• Analog vs. Digital• Analysis vs. Synthesis
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Signal definition
A function of one or more independent variables which conveys information on the nature of a physical phenomenon.
Examples:- Temperature vs. time- Closing value of a stock market vs. day
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𝑡
𝑥 (𝑡)
Cont..
: signal of one independent variable (e.g. time), is called dependent variable.
A common convention is to refer to the independent variable as time, although may in fact not.
is a signal of four independent variables.
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Modeling
Physical signal Mathematical function
Examples: Temperature of the room Stock Market Potentila difference between two points.
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System definition
An entity that manipulates one ore more signals to accomplish a function (job), thereby yielding new signals.
Any process or interaction of operations that transforms an input signal into an output signal with properties different from those of the input.
Examples:- Aircraft - Transmitter- Pen - Break system- Educational system - Car
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System representation
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𝑥 (𝑡) System 𝑦 (𝑡)Excitation signal Input: I
Response signal Output: O
SISO: Single-Input Single-Output
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Types of Systems
Systems are classified according to the number of inputs and outputs to:
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I1System O1
MIMO: Multi-Input Multi-Output
O2I2I3
I1System O
MISO: Multi-Input Single-Output
I2I3
I System
SIMO: Single-Input Multi-Output
O1O2O3
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Systems Modeling
Physical system Mathematical Equations
Example:
Integro-differential Equation
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Continuous-time vs. Discrete-time
The independent variable may be either continuous or discrete.
Continuous-time signals: defined at every instant of time over some time interval.
- where can take any real value.- may be 0 for a given range of values of .
Values for may be real or complex
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𝑡
𝑥 (𝑡)
𝑡 1 𝑡 2
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Cont..
t1, t2, and t3 are points of discontinuity.
CT is defined at a continuum points in time
A CT signal is not necessarily to be continuous at every point in time.
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CT
t1 t2 t3t
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Cont..
Discrete-time signals:defined at discrete points in time and not between them.
The independent variable takes only a discrete set of values. where
Values for may be real or complex
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𝑛
𝑥 [𝑛 ]
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Analog vs. Digital
The signal amplitude may be either continuous or discrete
At each time value, analog signal amplitude takes real or complex value (a.k.a. continuous-valued)
Digital signal amplitude takes values from a discrete set “finite number of values” (a.k.a. discrete-valued)
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Analog continuous-time signal
Digital continuous-time signal
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-1
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Reminder:
Finite set: has a beginning and an end and the number of elements is countable. Every finite set is countable e.g., {-1,0,1,2},
Infinite set: does not has start or end or has both start and end but is uncountable. e.g., infinite and countable: {…,2,4,6,8},{-1,1,3,5,7,…},{…,2,5,8,11,14,…}. e.g., infinite and uncountable:
If the signal’s amplitude (A) is a finite set the signal is Digital, otherwise it is Analog.
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Cont..
Example:
CT & DT: qualify the nature of the signal along the time (horizontal) axis.
Analog & Digital: qualify the nature of the signal along the amplitude (vertical) axis.
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𝑛-1
1
DT & DigitalAmplitude
𝑛
DT & AnalogAmplitude or Amplitude
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Continuous-time vs. Discrete-time system
Systems are classified according to the type of input signals and output signals.
Continuous-time system: all the signals are CT signals.
Discrete-time system: all the signals are DT signals.
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𝑥 (𝑡) System 𝑦 (𝑡)
𝑥 [𝑛 ] System 𝑦 [𝑛 ]
Analysis vs. Synthesis
Analysis: study the characteristics of a system to understand how it will response to various input signals.
Synthesis: design a system to achieve a desired outputs.
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Transformation
Time domain vs. Frequency domain Why Transformation? Real life examples:
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