Signals and Systems - Fatos Tunay Yarman Vural

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Résumé :

About the Authors xiii

Preface xiv

Acknowledgments xvii

About the Companion Website xix

1 Introduction to Systems and Signals 1

1.1 Example Applications 2

1.1.1 Three-Dimensional World Models by LIDAR Signals 3

1.1.2 Modeling the Brain Networks from the Brain Signals 3

1.1.3 Detecting the Buildings from the Remote-Sensed Satellite Images 4

1.1.4 Noise Reduction in Old Records 4

1.2 Relationship Between Signals and Systems 4

1.3 Mathematical Representation of Signals and Systems 5

1.3.1 Signals Represented by Functions 6

1.3.2 Types of Signals 6

1.3.3 Energy of a Signal 9

1.3.4 Power of a Signal 10

1.4 Operations on the Time Variable of Signals 10

1.4.1 Time Shift 11

1.4.2 Time Reverse 12

1.4.3 Time Scale 13

1.4.4 Time Scale and Shift 15

1.5 Signals with Symmetry Properties 19

1.5.1 Periodic Signals 21

1.5.1.1 Continuous Time Periodic Signals 22

1.5.1.2 Discrete Time Periodic Signals 23

1.5.2 Even and Odd Signals 24

1.6 Complex Signals Represented by Complex Functions 28

1.6.1 Complex Numbers Represented in Cartesian Coordinate System 28

1.6.2 Complex Numbers Represented in Polar Coordinate System and Euler's Number 30

1.6.3 Complex Functions 33

1.7 Chapter Summary 35

Problems 36

2 Basic Building Blocks of Signals 43

2.1 LEGO Functions of Signals 43

2.2 King of the Functions: Exponential Function 44

2.2.1 Real Exponential Function 44

2.2.1.1 Continuous Time Real Exponential Function 44

2.2.1.2 Discrete Time Real Exponential Function 46

2.2.2 Complex Exponential Function 47

2.2.2.1 Continuous Time Complex Exponential Functions 48

2.2.2.2 Harmonically Related Complex Exponential 49

2.2.2.3 Complex Exponential Function for Discrete Time Signals 53

2.3 Unit Impulse Function 55

2.3.1 Discrete Time Unit Impulse Function or Dirac-Delta Function 55

2.3.2 Continuous Time Unit Impulse Function 56

2.3.3 Comparison of Discrete Time and Continuous Time Unit Impulse Functions 57

2.4 Unit Step Function 58

2.4.1 Discrete Time Unit Step Function 58

2.4.2 Relationship Between the Discrete Time Unit Step and Unit Impulse Functions 58

2.4.3 Continuous Time Unit Step Function 60

2.4.4 Comparison of Discrete Time and Continuous Time Unit Step functions 61

2.4.4.1 Relationship Between the Continuous Time Unit Step and Unit Impulse Functions 61

2.5 Chapter Summary 65

Problems 65

3 Basic Building Blocks and Properties of Systems 69

3.1 Representation of Systems by Equations 69

3.2 Interconnection of Basic Systems: Series, Parallel, Hybrid, and Feedback Control Systems 70

3.2.1 Series Systems 70

3.2.2 Parallel Systems 71

3.2.3 Hybrid Systems 71

3.2.3.1 Feedback Control Systems 72

3.2.3.2 An Example of System Modeling: Neurons as a Subsystem of Human Brain 73

3.3 Properties of Systems 74

3.3.1 Memory 75

3.3.2 Causality 76

3.3.3 Invertibility 77

3.3.4 Stability 79

3.3.5 Time Invariance 80

3.3.6 Linearity and Superposition Property 81

3.4 Basic Building Blocks of Systems and Their Properties 85

3.4.1 Scalar Multiplier 85

3.4.2 Adder 85

3.4.3 Multiplier 85

3.4.4 Integrator 86

3.4.5 Differentiator 86

3.4.6 Unit Delay Operator 87

3.4.7 Unit Advance Operator 87

3.5 Chapter Summary 89

Problems 89

4 Representation of Linear Time-Invariant Systems by Impulse Response and Convolution Operation 95