Wavelets: From Math to Practice

✍ Scribed by Desanka P. Radunovic

• Publisher: Springer
• Year: 2009
• Tongue: English
• Leaves: 176
• Edition: 1
• Category: Library

✦ Synopsis

The method of wavelet transforms is one key tool in signal processing and control. Modern wavelet theory defines outlines for construction of wavelets and transformations using them. It gives rules that one has to obey to get a wavelet basis with desired properties, meaning that everyone can create a wavelet adequate for the given task. This book helps to understanding this rules.

In seven chapters, the book gives a concise understanding of the theory of wavelets, explains how to compute them in practise and finally presents typical applications of wavelets and how they work. The book is written for graduate students and practising Engineers of electrical communications, signal processing and control.

✦ Table of Contents

Cover......Page 1
Wavelets: From Math to Practice......Page 2
Copyright - ISBN: 3642006132......Page 3
Preface......Page 8
Table of contents
......Page 10
List of Figures......Page 12
1 Introduction
......Page 14
2.1 Basic notations and properties......Page 20
2.2 Fourier analysis......Page 25
2.3 Fourier transform......Page 33
3.1 Multiresolution analysis......Page 48
3.2 Function decomposition......Page 52
3.3 Pyramid algorithm......Page 58
3.4 Construction of rnultiresolution......Page 60
4 Wavelets......Page 68
4.1 Dilatation equation......Page 69
4.2 Frequency domain......Page 72
4.3 Matrix interpretation......Page 76
4.4 Properties......Page 82
4.5 Convergence......Page 88
5.1 Discrete wavelet transform......Page 96
5.2 Daubechies wavelets......Page 106
5.3 Biorthogonal wavelets......Page 108
5.4 Cardinal B-splines......Page 111
5.5 Interpolation wavelets......Page 118
5.6 Second generation wavelets......Page 124
5.7 Nonstandard wavelets......Page 129
6.1 Signal......Page 136
6.2 Filter......Page 139
6.3 Orthogonal filter bank......Page 144
6.4 Daubechies filters......Page 151
6.5 Filter properties important for wavelets......Page 157
7.1 Signal and image processing......Page 162
7.2 Numerical modeling......Page 166
Bibliography......Page 170
Index......Page 174