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The Laplace Transform M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl 1.

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Presentation on theme: "The Laplace Transform M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl 1."— Presentation transcript:

1 The Laplace Transform M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl 1

2 Generalizing the Fourier Transform M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl2

3 Generalizing the Fourier Transform M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl3

4 Generalizing the Fourier Transform M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl4

5 Complex Exponential Excitation M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl5

6 Complex Exponential Excitation M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl6

7 Pierre-Simon Laplace 3/23/1749 - 3/2/1827 M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl7

8 The Transfer Function M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl8

9 The Transfer Function M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl9

10 Cascade-Connected Systems M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl10

11 Direct Form II Realization M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl11

12 Direct Form II Realization M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl12

13 Direct Form II Realization M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl13

14 Direct Form II Realization M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl14

15 Direct Form II Realization M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl15

16 Direct Form II Realization M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl16

17 Inverse Laplace Transform M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl17

18 Existence of the Laplace Transform Time Limited Signals M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl18

19 Existence of the Laplace Transform M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl19

20 Existence of the Laplace Transform Right- and Left-Sided Signals Right-SidedLeft-Sided M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl20

21 Existence of the Laplace Transform Right- and Left-Sided Exponentials Right-SidedLeft-Sided M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl21

22 Existence of the Laplace Transform Right-Sided Exponential M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl22

23 Existence of the Laplace Transform Left-Sided Exponential M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl23

24 Existence of the Laplace Transform M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl24

25 Existence of the Laplace Transform M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl25

26 Laplace Transform Pairs M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl26

27 Region of Convergence M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl27

28 Region of Convergence Some of the most common Laplace transform pairs (There is more extensive table in the book.) M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl28

29 Laplace Transform Example M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl29

30 Laplace Transform Example M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl30

31 Laplace Transform Example M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl31

32 Laplace Transform Example M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl32

33 MATLAB System Objects M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl33

34 MATLAB System Objects M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl34

35 Partial-Fraction Expansion M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl35

36 Partial-Fraction Expansion M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl36

37 Partial-Fraction Expansion M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl37

38 Partial-Fraction Expansion M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl38

39 Partial-Fraction Expansion M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl39

40 Partial-Fraction Expansion M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl40

41 Partial-Fraction Expansion M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl41

42 Partial-Fraction Expansion M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl42

43 Partial-Fraction Expansion M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl43

44 Inverse Laplace Transform Example M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl44

45 Inverse Laplace Transform Example M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl45

46 Inverse Laplace Transform Example M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl46

47 Inverse Laplace Transform Example M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl47

48 Inverse Laplace Transform Example M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl48

49 Inverse Laplace Transform Example M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl49

50 Inverse Laplace Transform Example M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl50

51 Use of MATLAB in Partial Fraction Expansion M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl51

52 Laplace Transform Properties M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl52

53 Laplace Transform Properties M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl53

54 Laplace Transform Properties M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl54

55 Laplace Transform Properties M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl55

56 Final Value Theorem Laplace Transform Properties M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl56

57 Use of Laplace Transform Properties M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl57

58 Use of Laplace Transform Properties M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl58

59 The Unilateral Laplace Transform M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl59

60 The Unilateral Laplace Transform M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl60

61 The Unilateral Laplace Transform M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl61

62 The Unilateral Laplace Transform M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl62

63 The Unilateral Laplace Transform M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl63

64 The Unilateral Laplace Transform M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl64

65 The Unilateral Laplace Transform M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl65

66 Pole-Zero Diagrams and Frequency Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl66

67 Pole-Zero Diagrams and Frequency Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl67

68 Pole-Zero Diagrams and Frequency Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl68

69 Pole-Zero Diagrams and Frequency Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl69

70 Pole-Zero Diagrams and Frequency Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl70

71 Pole-Zero Diagrams and Frequency Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl71

72 Pole-Zero Diagrams and Frequency Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl72

73 Pole-Zero Diagrams and Frequency Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl73

74 Pole-Zero Diagrams and Frequency Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl74

75 Pole-Zero Diagrams and Frequency Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl75

76 Pole-Zero Diagrams and Frequency Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl76

77 Pole-Zero Diagrams and Frequency Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl77


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