1. Time-Domain System Analysis M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl 1

2. Continuous Time M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl2

3. Impulse Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl3

4. Impulse Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl4

5. Impulse Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl5

6. Impulse Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl6

7. Impulse Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl7

8. Impulse Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl8

9. Impulse Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl9

10. Impulse Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl10

11. Impulse Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl11

12. Impulse Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl12

13. Impulse Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl13

14. Impulse Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl14

15. The Convolution Integral Exact Excitation Approximate Excitation M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl15

16. The Convolution Integral M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl16

17. The Convolution Integral M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl17

18. The Convolution Integral M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl18

19. The Convolution Integral M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl19

20. The Convolution Integral M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl20

21. The Convolution Integral M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl21

22. The Convolution Integral M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl22

23. The Convolution Integral M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl23

24. The Convolution Integral M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl24

25. The Convolution Integral M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl25

26. A Graphical Illustration of the Convolution Integral M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl26

27. A Graphical Illustration of the Convolution Integral M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl27

28. A Graphical Illustration of the Convolution Integral M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl28

29. A Graphical Illustration of the Convolution Integral M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl29

30. A Graphical Illustration of the Convolution Integral M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl30

31. A Graphical Illustration of the Convolution Integral The process of convolving to find y(t) is illustrated below. M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl31

32. A Graphical Illustration of the Convolution Integral M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl32

33. A Graphical Illustration of the Convolution Integral M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl33

34. Convolution Example M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl34

35. Convolution Example M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl35

36. Convolution Integral Properties M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl36

37. The Unit Triangle Function The unit triangle, is the convolution of a unit rectangle with Itself. M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl37

38. System Interconnections If the output signal from a system is the input signal to a second system the systems are said to be cascade connected. It follows from the associative property of convolution that the impulse response of a cascade connection of LTI systems is the convolution of the individual impulse responses of those systems. Cascade Connection M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl38

39. System Interconnections If two systems are excited by the same signal and their responses are added they are said to be parallel connected. It follows from the distributive property of convolution that the impulse response of a parallel connection of LTI systems is the sum of the individual impulse responses. Parallel Connection M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl39

40. Unit Impulse Response and Unit Step Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl40

41. Stability and Impulse Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl41

42. Systems Described by Differential Equations M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl42

43. Systems Described by Differential Equations M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl43

44. Systems Described by Differential Equations M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl44

45. Systems Described by Differential Equations M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl45

46. MATLAB System Objects M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl46

47. MATLAB System Objects M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl47

48. Discrete Time M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl48

49. Impulse Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl49

50. Impulse Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl50

51. Impulse Response Example M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl51

52. Impulse Response Example M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl52

53. Impulse Response Example M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl53

54. Impulse Response Example M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl54

55. Impulse Response Example M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl55

56. Impulse Response Example M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl56

57. System Response Once the response to a unit impulse is known, the response of any LTI system to any arbitrary excitation can be found Any arbitrary excitation is simply a sequence of amplitude-scaled and time-shifted impulses Therefore the response is simply a sequence of amplitude-scaled and time-shifted impulse responses M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl57

58. Simple System Response Example M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl58

59. More Complicated System Response Example System Excitation System Impulse Response System Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl59

60. The Convolution Sum M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl60

61. A Convolution Sum Example M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl61

62. A Convolution Sum Example M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl62

63. A Convolution Sum Example M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl63

64. A Convolution Sum Example M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl64

65. Convolution Sum Properties M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl65

66. Convolution Sum Properties (continued) M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl66

67. Numerical Convolution M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl67

68. Numerical Convolution M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl68

69. Numerical Convolution M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl69

70. Numerical Convolution M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl70

71. Numerical Convolution M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl71

72. Stability and Impulse Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl72

73. System Interconnections The cascade connection of two systems can be viewed as a single system whose impulse response is the convolution of the two individual system impulse responses. This is a direct consequence of the associativity property of convolution. M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl73

74. System Interconnections The parallel connection of two systems can be viewed as a single system whose impulse response is the sum of the two individual system impulse responses. This is a direct consequence of the distributivity property of convolution. M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl74

75. Unit Impulse Response and Unit Sequence Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl75

76. Systems Described by Difference Equations M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl76

77. Systems Described by Difference Equations M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl77

78. Frequency Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl78

79. Frequency Response M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl79

80. Frequency Response Example M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl80

81. Frequency Response Example M. J. Roberts - All Rights Reserved. Edited by Dr. Robert Akl81