小波导论

1. An Overview

1.1 From Fourier analysm to wavelet analysm

1.2 The integral wavelet transform and time-frequency analysis

1.3 Inversion formulas and duals

1.4 Classification of wavelets

1.5 Multiresolution analysis， splines， and wavelets

1.6 Wavelet decompositions and reconstructions

2. Fourier Analysis

2.1 Fourier and inverse Fourier transforms

2.2 Continuous-time convolution and the delta function

2.3 Fourier transform of square-integrable functions

2.4 Fourier series

2.5 Basic convergence theory and Poissons summation formula

3. Wavelet Transforms and Time-Frequency Analysis

3.1 The Gabor transform

3.2 Short-time Fourier transforms and the Uncertainty Principle

3.3 The integral wavelet transform

3.4 Dyadic wavelets and inversions

3.5 Frames

3.6 Wavelet series

4. Cardinal Spline Analysis

4.1 Cardinal spline spaces

4.2 B-splines and their basic properties

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

4.4 B-net representations and computation of cardinal splines

4.5 Construction of spline approximation formulas

4.6 Construction of spline interpolation formulas

5. Scaling Functions and Wavelets

5.1 Multiresolution analysis

5.2 Scaling functions with finite two-scale relations

5 3 Direct-sum decompositions of L2(R)

5.4 Wavelets and their duals

5 5 Linear-phase filtering

5.6 Compactly supported wavelets

6. Cardinal Spline-Wavelets

6.1 Interpolatory spline-wavelets

6 2 Compactly supported spline-wavelets 182

6.3 Computation of cardinal spline-wavelets

6.4 EulerFrobeniuspolynomials

6.5 Error analysis in spline wavelet decomposition

6.6 Total positivity， complete oscillation， zero-crossings

7. Orthogonal Wavelets and Wavelet Packets

7.1 Examples of orthogonal wavelets

7.2 Identification of orthogonal two-scale symbols

7.3 Construction of compactly supported orthogonal wavelets

7.4 Orthogonal wavelet packets

7.5 Orthogonal decomposition of wavelet series

Notes

References

Subject Index

Appendix

《小波导论(英文版)》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。《小波导论(英文版)》内容安排由浅入深，算法推导详细，既有理论，又有应用背景。
《小波导论(英文版)》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。

《小波导论(英文版)》是小波分析方面奠基性的经典著作，已被翻译为多种语言，产生了深远影响。
《小波导论(英文版)》着重讲述样条小波和时频分析，内容安排由浅入深，算法推导详细，既有理论，又有应用背景。书中内容只要求读者具有函数论和实分析的一些基础知识，既适合初学者以及工程、技术方面人员学习，也是研究人员不可或缺的参考书。