EE 221 Signals Analysis and Systems Instructor: Dr. Ghazi Al Sukkar Dept. of Electrical Engineering The University of Jordan Email: ghazi.alsukkar@ju.edu.jo Fall 2014

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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