本书阐述了如何在信息处理、数值分析和数学建模中使用小波作为分析工具。本书把信号展开为基和框架,利用滤波器组作为算法描述。这种统一的观点填补了现有小波文献中的不足。本书给出经典信息处理问题的*新以点,特别强调从应用角度出发的信号压缩,涉及当前研究的*新成果。
本书可作为高年级本科生和研究生的教材,适用于信息处理、无线电通信、计算机科学和应用数学等专业,也适于从事相关领域的研究人员和从业人员阅读。

前言
1. Introduction to Wavelets.
1.1 Wavelets and Wavelet Expansion Systems
1.2 The Discrete Wavelet Transform
1.3 The Discrets-Time and Continuous Wavelet Transforms
1.4 Exercises and Experiments
1.5 This Chapter
2. A Multiresolution Formulation of Wavelet Systems.
2.1 Signal Spaces
2.2 The Scaling Function
2.3 The Wavelet Functions
2.4 The Discrete Wavelet Transform
2.5 A Parseveal's Theorem
2.6 Display of the Discrete Wavelet Transform and the Wavelet Expansion
2.7 Examples of Wavelet Expansions
2.8 An Example of the Haar Wavelet Syatem
3. Filter Banks and the Discrete Wavelet Transform.
3.1 Analysis-From Fine Scale to Coarse Scale
3.2 Synthesis-From Coarse Scale to Fine Scale
3.3 Input Coefficients
3.4 lattices and Lifting
3.5 Different points of View
4. Bases, Orthogonal Bases, Biorthogonal Bases, Frames, Tight Frames, and Unconditional Bases.
4.1 Bases,Orhogonal Bases,and Biorthogonal Bases
4.2 Frames and Tight Frames
4.3 Conditional and Unconditional Bases
5. The Scaling Function and Scaling Coefficients, Wavelet and Wavelet Coefficients.
5.1 Tools and Definitions
5.2 Necessary Conditions
5.3 Frequency Domain Necessary Conditions
5.4 Sufficient Conditions
5.5 The Wavelet
5.6 Alternate Normalizations
5.7 Example Scaling Functions and Wavelets
5.8 Further Properties of the Scaling Function and Wavelet
5.9 Parameterization of the Acaling coefficients
5.10 Calculation the Basic Function and Wavelet
6. Regularity, Moments, and Wavelet System Design.
……
7. Generalizations of the Basic Multiresolution Wavelet System.
8. Filter Banks and Transmultiplexers.
9. Calculation of the Discrete Wavelet Transform.
10. Wavelet-Based Signal Processing and Applications.
11. Summary Overview.
12. References.
Bibliography.
Appendix A. Derivations for Chapter 5 on Scaling Functions.
Appendix B. Derivations for Section on Properties.
Appendix C. Matlab Programs.
Index.

本书特点:以傅里叶方法为基础,逐步发展为更一般的方法;综合了数学和信号处理文献中与小波变换相关的内容;阐述了信号展开和滤波器组的方法;包含对基本小波系统的新的推广,包括M段小波、双正交系统、小波包和多小波;对具有有N阶算法复杂度的近似快速傅里叶变换算法级出小波的应用实例;包含其他小波文献的附加指南;附录中包含Matlab程序。