基本信息

内容简介

目录

基本信息

书名： 小波导论书号： 978-7-115-19557-9

原书名： An Introduction to Wavelets

原出版社： Academic Press

丛书名： 图灵原版数学统计学系列

分类： 数学与统计 >> 应用数学

作者： Charles K.Chui (崔锦泰)

出版日期： 2009-02-19

开本： 16开

页数： 276

内容简介

本书是一本小波分析的入门书，着重于样条小波和时频分析．书中基本内容有Fourier分析、小波变换、尺度函数、基数样条分析、基数样条小波、小波级数、正交小波和小波包．本书内容安排由浅入深，算法推导详细，既有理论，又有应用背景．

本书自成体系，只要求读者具有函数论和实分析的一些基础知识，适合作为高等院校理工科小波分析的入门教材，也适合科技工 作者用作学习小波的指导读物．

目录

Preface ix

1 An Overview 1

1.1 From Fourier analysm to wavelet analysm 1

1.2 The integral wavelet transform and time-frequency analysis 6

1.3 Inversion formulas and duals 9

1.4 Classification of wavelets 13

1.5 Multiresolution analysis, splines, and wavelets 16

1.6 Wavelet decompositions and reconstructions 18

2 Fourier Analysis 23

2.1 Fourier and inverse Fourier transforms 23

2.2 Continuous-time convolution and the delta function 27

2.3 Fourier transform of square-integrable functions 32

2.4 Fourier series 36

2.5 Basic convergence theory and Poisson's summation formula 43

3 Wavelet Transforms and Time-Frequency Analysis 49

3.1 The G abor transform 50

3.2 Short-time Fourier transforms and the Uncertainty Principle 54

3.3 The integral wavelet transform 60

3.4 Dyadic wavelets and inversions 64

3.5 Frames 68

3.6 Wavelet series 74

4 Cardinal Spline Analysis 81

4.1 Cardinal spline spaces 81

4.2 B-splines and their basic properties 85

4.3 The two-scale relation and an interpolatory graphical display algorithm 90

4.4 B-net representations and computation of cardinal splines 95

4.5 Construction of spline approximation formulas 100

4.6 Construction of spline interpolation formulas 109

5 Scaling Functions and Wavelets 119

5.1 Multiresolution analysis 120

5.2 Scaling functions with finite two-scale relations 128

5 3 Direct-sum decompositions of L2(l[t) 140

5.4 Wavelets and their duals 146

5 5 Linear-phase filtering 159

5.6 Compactly supported wavelets 168

6 Cardinal Spline-Wavelets 177

6.1 Interpolatory spline-wavelets 177

6 2 Compactly supported spline-wavelets 182

6.3 Computation of cardinal spline-wavelets 187

6.4 EulerFrobeniuspolynomials 195

6.5 Error analysis in spline wavelet decomposition 199

6.6 Total positivity, com ete oscillation, zero-crossings 207

7 Orthogonal Wavelets and Wavelet Packets 215

7.1 Examples of orthogonal wavelets 215

7.2 Identification of orthogonal two-scale symbols 220

7.3 Construction of compactly supported orthogonal wavelets 229

7.4 Orthogonal wavelet packets 236

7.5 Orthogonal decomposition of wavelet series 240

Notes 245

References 251

Subject Index 257

Appendix 265