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Introduction to System

Introduction to System. Hany Ferdinando Dept. of Electrical Engineering Petra Christian University. General Overview. What is system? How to classify systems? What is LTI system? System interconnection Differential and difference equation. x. System. y. Definition.

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Introduction to System

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  1. Introduction to System Hany Ferdinando Dept. of Electrical Engineering Petra Christian University

  2. General Overview • What is system? • How to classify systems? • What is LTI system? • System interconnection • Differential and difference equation Introduction to System - Hany Ferdinando

  3. x System y Definition A system is a part of environment that causes certain signals in that environment to be related System relates input and output. Usually, inputs are associated with causes and output with effects Introduction to System - Hany Ferdinando

  4. Classification • Causal and non-causal system • y(t) = x(t) + 2x(t-1) • y(t) = x(t+1) – x(t) + 3x(t-2) • Memory and memoryless system • y(t) = -4x(t-1) + 2x(t) • y(t) = 2x(t) • Lumped and distributed system • It is about the number of state… Introduction to System - Hany Ferdinando

  5. Two General Systems • Continuous-time system • It processes continuous-time signal • Discrete-time system • It processes discrete-time signal Introduction to System - Hany Ferdinando

  6. LTI System • All systems we discussed here are LTI • LTI is Linear Time-Invariant • The system has to be linear • The system has to be time-invariant • Non LTI systems are not discussed here…, sorry!! Introduction to System - Hany Ferdinando

  7. Linearity • A system is linear if and only if it fulfills homogeneity and additivity law • One can say that the superposition theorem can be applied • A linear system can be processed easier than non-linear system Introduction to System - Hany Ferdinando

  8. Linearity Test: • Homogeneity Law • If input u gives output y, then input au has to give output ay • Additivity law • If input u1 and u2 give output y1 and y2 respectively, then input (u1+u2) has to give output (y1+y2) • Combined! Examples and Exercises Introduction to System - Hany Ferdinando

  9. Time-invariant • It means the system does not depend on time • Delayed input will result delayed output Introduction to System - Hany Ferdinando

  10. Time-invariant test: u(n) u(n) System delay = y(n) u(n-m) delay System y(n-m) y(n-m) Examples and Exercises Introduction to System - Hany Ferdinando

  11. System 1 System 2 input output System Interconnection • It is series or cascade interconnection • The output of system 1 is the input to system 2 • Shortly, the output of the previous system is the input to the next system Introduction to System - Hany Ferdinando

  12. System 1 output input System 2 + System Interconnection • It is parallel interconnection • The input signal is applied to both system simultaneously • ‘+’ symbol means the output is sum of both output of system 1 and 2 • ‘.’ symbol means the signal is duplicated Introduction to System - Hany Ferdinando

  13. System Interconnection • We can combine both interconnections to form a system • Beside ‘+’ sign, we can also use ‘–’ sign • In the box of the system, we can put any process Introduction to System - Hany Ferdinando

  14. Multiply by 2 + + Square x(n) y(n) – Square Example… y(n) = (2x(n) – x(n)2)2 Introduction to System - Hany Ferdinando

  15. Delay • Delay is important in the linear system • One may need to delay signal before processing • Delay usually expresses in unit delay, it means it will delay one unit per block • For discrete-time system, delay is represented by Z-1 Introduction to System - Hany Ferdinando

  16. Differential Equation • Continuous-time system is expressed in the form of differential equation • The response of the system is the solution of that equation Introduction to System - Hany Ferdinando

  17. Difference Equation • Discrete-time system is expressed in the form of difference equation • Delay is used to express the difference • We can draw the difference equation in the system interconnection Introduction to System - Hany Ferdinando

  18. y(n) ¼ Z-1 Z-1 x(n) + ½ Difference Equation y(n) = ¼ x(n) + ½ y(n-2) Introduction to System - Hany Ferdinando

  19. Exercise • y(n) = 2x(n) – x(n-1) – ½ y(n-1) • y(n) = x(n-1) – x(n-2) + y(n-2) • y(n) = x(n) + x(n-1) + y(n-2) Introduction to System - Hany Ferdinando

  20. Next… The basic information about system is discussed. Now we will move to the next topic, i.e. operation on the system. Please read: • Signals and Systems by Alan V. Oppehnheim, chapter 3, p 69-94 • Signals and Linear Systems by Robert A. Gabel, chapter 2, p46-68, chapter 3, p 129-138 Introduction to System - Hany Ferdinando

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