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Fourier Analysis

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This book aims to learn to use the basic concepts in signal processing. Each chapter is a reminder of the basic principles is pres... Lire la suite
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Description

This book aims to learn to use the basic concepts in signal processing. Each chapter is a reminder of the basic principles is presented followed by a series of corrected exercises. After resolution of these exercises, the reader can pretend to know those principles that are the basis of this theme. 'We do not learn anything by word, but by example.'

Auteur

JL Gautier was a university professor at ENSEA. He retired in 2014. He taught the design of microwave circuits and architecture segments RF digital communications systems. His research activities have focused on the design of integrated monolithic microwave circuits. He is the author of over 100 publications and papers in journals and international conferences.

R Ceschi is the General Director of Esigetel and the Deputy Director General of Efrei Parsi-south group.
He teaches theory and signal optimization in engineering schools and abroad.
Associate Professsor at the "Cape Peninsula University of Technology" at the "Shanghai Normal University"
Visiting Professor at the "Beijing Institute of Technology" and at the "Beijing Institute of Petrochemical Technology"



Contenu

Preface xi

Chapter 1. Fourier Series 1

1.1. Theoretical background 1

1.1.1. Orthogonal functions 1

1.1.2. Fourier Series 3

1.1.3. Periodic functions 5

1.1.4. Properties of Fourier series 6

1.1.5. Discrete spectra. Power distribution 8

1.2. Exercises 9

1.2.1. Exercise 1.1. Examples of decomposition calculations 10

1.2.2. Exercise 1.2 11

1.2.3. Exercise 1.3 12

1.2.4. Exercise 1.4 12

1.2.5. Exercise 1.5 12

1.2.6. Exercise 1.6. Decomposing rectangular functions 13

1.2.7. Exercise 1.7. Translation and composition of functions 14

1.2.8. Exercise 1.8. Time derivation of a function 15

1.2.9. Exercise 1.9. Time integration of functions 15

1.2.10. Exercise 1.10 15

1.2.11. Exercise 1.11. Applications in electronic circuits 16

1.3. Solutions to the exercises 17

1.3.1. Exercise 1.1. Examples of decomposition calculations 17

1.3.2. Exercise 1.2 25

1.3.3. Exercise 1.3 26

1.3.4. Exercice 1.4 26

1.3.5. Exercise 1.5 27

1.3.6. Exercise 1.6 27

1.3.7. Exercise 1.7. Translation and composition of functions 29

1.3.8. Exercise 1.8. Time derivation of functions 31

1.3.9. Exercise 1.9. Time integration of functions 32

1.3.10. Exercise 1.10 32

1.3.11. Exercise 1.11 35

Chapter 2. Fourier Transform 39

2.1. Theoretical background 39

2.1.1. Fourier transform 39

2.1.2. Properties of the Fourier transform 42

2.1.3. Singular functions 46

2.1.4. Fourier transform of common functions 51

2.1.5. Calculating Fourier transforms using the Dirac impulse method 53

2.1.6. Fourier transform of periodic functions 54

2.1.7. Energy density 54

2.1.8. Upper limits to the Fourier transform 55

2.2. Exercises 56

2.2.1. Exercise 2.1 56

2.2.2. Exercise 2.2 57

2.2.3. Exercise 2.3 58

2.2.4. Exercise 2.4 59

2.2.5. Exercise 2.5 59

2.2.6. Exercise 2.6 59

2.2.7. Exercise 2.7 60

2.2.8. Exercise 2.8 60

2.2.9. Exercise 2.9 61

2.2.10. Exercise 2.10 62

2.2.11. Exercise 2.11 62

2.2.12. Exercise 2.12 63

2.2.13. Exercise 2.13 63

2.2.14. Exercise 2.14 64

2.2.15. Exercise 2.15 64

2.2.16. Exercise 2.16 65

2.2.17. Exercise 2.17 66

2.3. Solutions to the exercises 67

2.3.1. Exercise 2.1 67

2.3.2. Exercise 2.2 68

2.3.3. Exercise 2.3 74

2.3.4. Exercise 2.4 74

2.3.5. Exercise 2.5 76

2.3.6. Exercise 2.6 76

2.3.7. Exercise 2.7 77

2.3.8. Exercise 2.8 79

2.3.9. Exercise 2.9 82

2.3.10. Exercise 2.10 85

2.3.11 Exercise 2.11 86

2.3.12 Exercise 2.12 88

2.3.13 Exercise 2.13 91

2.3.14 Exercise 2.14 91

2.3.15 Exercice 2.15 92

2.3.16 Exercise 2.16 94

2.3.17 Exercise 2.17 95

Chapter 3. Laplace Transform 97

3.1. Theoretical background 97

3.1.1. Definition 97

3.1.2. Existence of the Laplace transform 98

3.1.3. Properties of the Laplace transform 98

3.1.4. Final value and initial value theorems 102

3.1.5. Determining reverse transforms 102

3.1.6. Approximation methods 105

3.1.7. Laplace transform and differential equations 107

3.1.8. Table of common Laplace transforms 108

3.1.9. Transient state and steady state 110

3.2. Exercise instruction 111

3.2.1. Exercise 3.1 111

3.2.2. Exercise 3.2 111

3.2.3. Exercise 3.3 112

3.2.4. Exercise 3.4 112

3.2.5. Exercise 3.5 112

3.2.6. Exercise 3.6 113

Informations sur le produit

Titre: Fourier Analysis
Auteur:
Code EAN: 9781119372233
ISBN: 978-1-119-37223-3
Protection contre la copie numérique: Adobe DRM
Format: eBook (epub)
Editeur: Wiley-Iste
Genre: Autres
nombre de pages: 266
Parution: 18.01.2017
Année: 2017
Sous-titre: Englisch
Taille de fichier: 13.9 MB