小波導論

本書自成體系，只要求讀者具有函式論和實分析的一些基礎知識，適合作為高等院校理工科小波分析的入門教材，也適合科技工 作者用作學習小波的指導讀物．

基本介紹

• 書名：小波導論
• 作者：Charles K.Chui (崔錦泰)
• 原版名稱：An Introduction to Wavelets
• ISBN：9787115195579
• 頁數：276頁
• 出版時間：2009-02-19
• 開本：16開
• 原出版社：Academic Press
• 叢書名：圖靈原版數學統計學系列
• 分類： 數學與統計 >> 套用數學

書籍介紹

本書是一本小波分析的入門書，著重於樣條小波和時頻分析．書中基本內容有Fourier分析、小波變換、尺度函式、基數樣條分析、基數樣條小波、小波級數、正交小波和小波包．本書內容安排由淺入深，算法推導詳細，既有理論，又有套用背景．

目錄

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