1. EE 221 Signals Analysis and Systems
Instructor: Dr. Ghazi Al Sukkar
Dept. of Electrical Engineering
The University of Jordan
Fall 2014

2. Course Details Objective Grading Text Book
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

3. 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

4. Course Website http://academic.ju.edu.jo/ghazi.alsukkar/default.aspx

5. Outline Introduction Signals, Systems and Transforms:
Signal Definition
System definition
Continuous-time vs. Discrete-time
Analog vs. Digital
Analysis vs. Synthesis
Fall 2014

6. 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
𝑥(𝑡) 𝑡
Fall 2014

7. Cont..
𝑥(𝑡): signal of one independent variable 𝑡 (e.g. time), 𝑥 is called dependent variable.
A common convention is to refer to the independent variable as time, although may in fact not.
𝑓(𝑡,𝑥,𝑦,𝑧) is a signal of four independent variables.
Fall 2014

8. Modeling Physical signal 𝑀𝑜𝑑𝑒𝑙𝑖𝑛𝑔 Mathematical function Examples:
Temperature of the room
Stock Market
Potentila difference between two points.
Fall 2014

9. 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
Fall 2014

10. System representation
SISO: Single-Input Single-Output
System
𝑥(𝑡)
𝑦(𝑡)
Excitation signal Input: I
Response signal Output: O
Fall 2014

11. Types of Systems System System System
Systems are classified according to the number of inputs and outputs to:
MIMO: Multi-Input Multi-Output I1
System O1 I2 O2 I3
MISO: Multi-Input Single-Output I1
System I2 O I3
SIMO: Single-Input Multi-Output
System O1 I O2 O3
Fall 2014

12. Systems Modeling Example:
Physical system 𝑀𝑜𝑑𝑒𝑙𝑖𝑛𝑔 Mathematical Equations
Example:
𝑅 𝑖 𝑡 +𝐿 𝑑𝑖(𝑡) 𝑑𝑡 + 1 𝐶 −∞ 𝑡 𝑖 𝜏 𝑑𝜏 =𝑣(𝑡) Integro-differential Equation
Fall 2014

13. 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.
- 𝑥(𝑡) where 𝑡 can take any real value.
- 𝑥(𝑡) may be 0 for a given range of values of 𝑡.
Values for 𝒙 may be real or complex 𝑡
𝑥(𝑡) 𝑡1 𝑡2
Fall 2014

14. Cont.. CT t1, t2, and t3 are points of discontinuity.
CT is defined at a continuum points in time ⇒𝑡∈ℝ, ℝ:𝑠𝑒𝑡 𝑜𝑓 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠.
A CT signal is not necessarily to be continuous at every point in time. CT t1 t2 t3 t
Fall 2014

15. Cont.. Discrete-time signals:
defined at discrete points in time and not between them.
The independent variable takes only a discrete set of values.
𝑥[𝑛] where 𝑛 ∈ℤ= …−3,−2,−1,0,1,2,3…
Values for 𝑥 may be real or complex 𝑛
𝑥[𝑛]
Fall 2014

16. Analog continuous-time signal Digital continuous-time signal
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)
Analog continuous-time signal
Digital continuous-time signal 1 -1
Fall 2014

17. 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}, 𝑥∈ℤ:−2<𝑥≤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: 𝑥∈ℝ:−2<𝑥≤2
If the signal’s amplitude (A) is a finite set ⟹ the signal is Digital, otherwise it is Analog.
Fall 2014

18. Cont.. Example: DT & Digital Amplitude ∈{−1,0,1,2} 1 𝑛 -1 DT & Analog
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.
DT & Digital
Amplitude ∈{−1,0,1,2} 𝑛 -1 1
DT & Analog
Amplitude ∈ℝ
or Amplitude ∈ 𝐴|−2<𝐴≤3 𝑛
Fall 2014

19. 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.
𝑥(𝑡)
System
ℎ(𝑡)
𝑦(𝑡)
𝑥[𝑛]
System
ℎ[𝑛]
𝑦[𝑛]
Fall 2014

20. 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.
Fall 2014

21. Transformation Time domain vs. Frequency domain Why Transformation?
Real life examples:
Fall 2014