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Signals and Systems Prof. Wonhee Kim Chapter 1

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Page 1: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

Signals and Systems

Prof. Wonhee KimChapter 1

Page 2: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

CONTINUOUS-TIME AND DISCRETE-TIME SIGNALS

Systems and Signal

2

Page 3: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

CONTINUOUS-TIME AND DISCRETE-TIME SIGNALS

3

Page 4: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

CONTINUOUS-TIME AND DISCRETE-TIME SIGNALS

4

Page 5: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

Signal Energy and Power

5

Page 6: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

Simple physical system

Continuous time signal

Discrete time signal

Signal Energy and Power

6

Page 7: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

Simple physical system

Continuous time signal

Discrete time signal

Signal Energy and Power

7

Page 8: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

Simple physical system

Continuous time signal

Discrete time signal

Signal Energy and Power

8

Page 9: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

Simple physical system

Signal Energy and Power

9

Page 10: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

TRANSFORMATIONS OF THE INDEPENDENT VARIABLE

10

Page 11: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

TRANSFORMATIONS OF THE INDEPENDENT VARIABLE

11

Page 12: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

TRANSFORMATIONS OF THE INDEPENDENT VARIABLE

12

Page 13: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

TRANSFORMATIONS OF THE INDEPENDENT VARIABLE

13

Page 14: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

TRANSFORMATIONS OF THE INDEPENDENT VARIABLE

14

Periodic signals

Page 15: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

TRANSFORMATIONS OF THE INDEPENDENT VARIABLE

15

Periodic signals

Page 16: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

TRANSFORMATIONS OF THE INDEPENDENT VARIABLE

16

Even and Odd Signals Even signals

Odd signals

Page 17: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

TRANSFORMATIONS OF THE INDEPENDENT VARIABLE

17

Even and Odd Signals

Page 18: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

TRANSFORMATIONS OF THE INDEPENDENT VARIABLE

18

Even and Odd Signals

Page 19: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

EXPONENTIAL AND SINUSOIDAL SIGNALS

19

Continuous-Time Complex Exponential and Sinusoidal Signals Real Exponential Signals

Page 20: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

EXPONENTIAL AND SINUSOIDAL SIGNALS

20

Continuous-Time Complex Exponential and Sinusoidal Signals Periodic Complex Exponential and Sinusoidal Signals

Page 21: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

EXPONENTIAL AND SINUSOIDAL SIGNALS

21

Continuous-Time Complex Exponential and Sinusoidal Signals Fundamental frequency and period

Page 22: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

EXPONENTIAL AND SINUSOIDAL SIGNALS

22

Continuous-Time Complex Exponential and Sinusoidal Signals Periodic Complex Exponential and Sinusoidal Signals

Page 23: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

EXPONENTIAL AND SINUSOIDAL SIGNALS

23

Continuous-Time Complex Exponential and Sinusoidal Signals Periodic Complex Exponential and Sinusoidal Signals

Page 24: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

EXPONENTIAL AND SINUSOIDAL SIGNALS

24

Continuous-Time Complex Exponential and Sinusoidal Signals Periodic Complex Exponential and Sinusoidal Signals

Page 25: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

EXPONENTIAL AND SINUSOIDAL SIGNALS

25

Continuous-Time Complex Exponential and Sinusoidal Signals Periodic Complex Exponential and Sinusoidal Signals

Page 26: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

EXPONENTIAL AND SINUSOIDAL SIGNALS

26

Continuous-Time Complex Exponential and Sinusoidal Signals Periodic Complex Exponential and Sinusoidal Signals

Page 27: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

EXPONENTIAL AND SINUSOIDAL SIGNALS

27

Continuous-Time Complex Exponential and Sinusoidal Signals General Complex Exponential Signals

Page 28: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

EXPONENTIAL AND SINUSOIDAL SIGNALS

28

Continuous-Time Complex Exponential and Sinusoidal Signals General Complex Exponential Signals

Page 29: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

EXPONENTIAL AND SINUSOIDAL SIGNALS

29

Discrete-Time Complex Exponential and Sinusoidal Signals

Page 30: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

EXPONENTIAL AND SINUSOIDAL SIGNALS

30

Discrete-Time Complex Exponential and Sinusoidal Signals Real Exponential Signals

Page 31: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

EXPONENTIAL AND SINUSOIDAL SIGNALS

31

Discrete-Time Complex Exponential and Sinusoidal Signals Sinusoidal Signals

Page 32: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

EXPONENTIAL AND SINUSOIDAL SIGNALS

32

Discrete-Time Complex Exponential and Sinusoidal Signals Sinusoidal Signals

Page 33: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

EXPONENTIAL AND SINUSOIDAL SIGNALS

33

Discrete-Time Complex Exponential and Sinusoidal Signals General Complex Exponential Signals

Page 34: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

EXPONENTIAL AND SINUSOIDAL SIGNALS

34

Periodicity Properties of Discrete-Time Complex Exponentials

Page 35: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

THE UNIT IMPULSE AND UNIT STEP FUNCTIONS

35

Discrete-Time Unit Impulse

Unit Step Sequences

Page 36: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

THE UNIT IMPULSE AND UNIT STEP FUNCTIONS

36

Discrete-Time Unit Impulse and Unit Step Sequences

Page 37: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

THE UNIT IMPULSE AND UNIT STEP FUNCTIONS

37

Discrete-Time Unit Impulse and Unit Step Sequences

Page 38: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

THE UNIT IMPULSE AND UNIT STEP FUNCTIONS

38

Discrete-Time Unit Impulse and Unit Step Sequences

Page 39: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

THE UNIT IMPULSE AND UNIT STEP FUNCTIONS

39

Continuous-Time Unit Step

Unit Impulse Functions

Page 40: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

THE UNIT IMPULSE AND UNIT STEP FUNCTIONS

40

Unit Impulse Functions

Page 41: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

THE UNIT IMPULSE AND UNIT STEP FUNCTIONS

41

Unit Impulse Functions

Page 42: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

THE UNIT IMPULSE AND UNIT STEP FUNCTIONS

42

Unit Impulse Functions

Page 43: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

THE UNIT IMPULSE AND UNIT STEP FUNCTIONS

43

Unit Impulse Functions

Page 44: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

THE UNIT IMPULSE AND UNIT STEP FUNCTIONS

44

Unit Impulse Functions

Page 45: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

CONTINUOUS-TIME AND DISCRETE-TIME SYSTEMS

45

Page 46: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

CONTINUOUS-TIME AND DISCRETE-TIME SYSTEMS

46

Continuous-time system

Page 47: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

CONTINUOUS-TIME AND DISCRETE-TIME SYSTEMS

47

Continuous-time system

Page 48: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

CONTINUOUS-TIME AND DISCRETE-TIME SYSTEMS

48

Discrete-time system

Page 49: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

CONTINUOUS-TIME AND DISCRETE-TIME SYSTEMS

49

Interconnections of Systems

Page 50: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

CONTINUOUS-TIME AND DISCRETE-TIME SYSTEMS

50

Interconnections of Systems

Page 51: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

CONTINUOUS-TIME AND DISCRETE-TIME SYSTEMS

51

Interconnections of Systems

Page 52: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

BASIC SYSTEM PROPERTIES

52

Systems with and without Memory

Page 53: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

BASIC SYSTEM PROPERTIES

53

Systems with and without Memory

Page 54: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

BASIC SYSTEM PROPERTIES

54

Systems with and without Memory

Page 55: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

BASIC SYSTEM PROPERTIES

55

Systems with and without Memory

Page 56: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

BASIC SYSTEM PROPERTIES

56

lnvertibility and Inverse Systems

Page 57: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

BASIC SYSTEM PROPERTIES

57

Causality

Page 58: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

BASIC SYSTEM PROPERTIES

58

Causality

Page 59: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

BASIC SYSTEM PROPERTIES

59

Stability

Page 60: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

BASIC SYSTEM PROPERTIES

60

Stability

Page 61: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

BASIC SYSTEM PROPERTIES

61

Stability

Page 62: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

BASIC SYSTEM PROPERTIES

62

Stability

Page 63: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

BASIC SYSTEM PROPERTIES

63

Time Invariant

Page 64: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

BASIC SYSTEM PROPERTIES

64

Linearity

Page 65: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

BASIC SYSTEM PROPERTIES

65

Linearity

Page 66: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

BASIC SYSTEM PROPERTIES

66

Linearity

Page 67: Chapter 1 · Simple physical system Continuous time signal Discrete time signal Signal Energy and Power 6

BASIC SYSTEM PROPERTIES

67

Linearity