EE 221Signals Analysis and Systems

Instructor: Dr. Ghazi Al SukkarDept. of Electrical EngineeringThe University of JordanEmail: ghazi.alsukkar@ju.edu.jo

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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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