Signal Processing Applications in Mechatronics

... konulu sunumlar: "Signal Processing Applications in Mechatronics"— Sunum transkripti:

1 Signal Processing Applications in Mechatronics
Assist. Prof. Hülya Yalçın Tel : ext:2580 Class hours : Monday 9:30- 12:30 Office hours : Monday 14:30- 16:30 and anytime through Address : Room 311 in Gümüşsuyu Campus

2 Signals Hülya Yalçın ©

3 Continuous-time and discrete-time signals
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4 What is a system? Hülya Yalçın ©

5 Today’s lecture: Hülya Yalçın ©

6 Linearity Hülya Yalçın ©

7 Time-invariance Hülya Yalçın ©

8 Linear time-invariant (LTI) systems
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9 Linear System Models - I
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10 Linear System Models - II
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11 Linear System Models - III
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12 Linear System Models - IV
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13 Unit Step , Unit Ramp Hülya Yalçın ©

14 Unit Impulse Hülya Yalçın ©

15 Main Property of Unit Impulse
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16 Transformations of time
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17 Examples Hülya Yalçın ©

18 Shifted Unit Impulse and the Sifting Property
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19 Basic Discrete-time Signals
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20 Periodic Continuous-time Signals
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21 Periodic Discrete-time Signals
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22 Next Hülya Yalçın ©

23 What is a system? Hülya Yalçın ©

24 Causality Hülya Yalçın ©

25 Memory Hülya Yalçın ©

26 Linearity Hülya Yalçın ©

27 Linearity – example 1 Hülya Yalçın ©

28 Linearity – example 2 Hülya Yalçın ©

29 Linearity – example 3 Hülya Yalçın ©

30 Linearity – example 4 Hülya Yalçın ©

31 Time - Invariance Hülya Yalçın ©

32 Time – Invariance : Example 1
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33 Time – Invariance : Example 2
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34 Time – Invariance : Example 3
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35 Linear time-invariant (LTI) systems
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36 LTI systems via differential equations
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37 The Unit Pulse Response
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38 The Unit Pulse Response - continued
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39 Convolution Representation
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40 Convolution of discrete-time signals
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41 Useful properties of Convolution
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42 Convolution Representation
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43 Computing Discrete Convolution: flip and shift
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44 Computing Discrete Convolution: example
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45 Computing Discrete Convolution: example cont’
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46 Convolution representation of continuous-time systems
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47 The unit impulse response
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48 The shifted unit impulse response
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49 Derivation of the convolution representation
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50 Derivation of the convolution representation
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51 Derivation of the convolution representation
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52 Convolution of continuous-time signals
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53 Additional properties of the convolution
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54 Computing convolution integrals: example 1
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55 Computing convolution integrals: example 2
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56 Computing convolution integrals: example 2
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57 Computing convolution integrals: example 2
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58 Hülya Yalçın ©

59 Hülya Yalçın ©

60 Hülya Yalçın ©

61 Hülya Yalçın ©

62 Hülya Yalçın ©

63 Hülya Yalçın ©

64 Hülya Yalçın ©

65 Fourier Series Hülya Yalçın ©

66 Review: vectors Hülya Yalçın ©

67 Vector Spaces Hülya Yalçın ©

68 Signal Spaces Hülya Yalçın ©

69 The space of periodic signals
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70 Complete orthonormal sets of functions
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71 Fourier Series Hülya Yalçın ©

72 Fourier Coefficients Hülya Yalçın ©

73 Convergence of Fourier Series
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74 Trigonometric Fourier Series
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75 Trigonometric Fourier Series
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76 Trigonometric Fourier Series
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77 Symmetry Properties Hülya Yalçın ©

78 Trigonometric Fourier series: example
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79 Trigonometric Fourier series: example
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80 Complex Exponential Fourier Series
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81 Complex Exponential Fourier Series
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82 Symmetry Properties for real signals
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83 Amplitude and phase spectra
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84 Fourier Transform Hülya Yalçın ©

85 Recap: Fourier Series Hülya Yalçın ©

86 Spectral content of aperiodic signals: the Fourier transform
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87 Example: rectangular pulse
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88 Inverse Fourier Transform
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89 Hülya Yalçın ©

90 Properties of Fourier Transform
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91 Properties of Fourier Transform: Linearity
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92 Properties of Fourier Transform: Time-shift
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93 Multiplication by a complex exponential
Multiplication by a cosine Hülya Yalçın ©

94 Convolution in time-domain
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95 Parseval’s Theorem Hülya Yalçın ©

96 Duality Example Hülya Yalçın ©

97 Generalized Fourier Transform
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98 Fourier Transform of cosine
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99 Fourier transform of a periodic signal
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100 Bandlimited and timelimited signals
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101 Frequency response of LTI systems
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