小波与小波变换导论（英文版）|经典原版书库|（美）C.西德尼·伯罗斯（C.Sidney Burrus）等|机械工业出版社

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小波与小波变换导论（英文版）

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原书名：Introduction to Wavelets and Wavelet Transforms:A Primer	原出版社：Prentice Hall/Pearson
作者：（美）C.西德尼·伯罗斯（C.Sidney Burrus）等	出版社：机械工业出版社
译者：	丛书名：经典原版书库
出版日期：2005-4-1	上架日期：2005-10-8
ISBN：711115911X	页数：版次：1-2
开本：16开	装帧：

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| 大封面 | 封底 | 前言 | 内容简介 | 序言 | 目录 | 作者简介 | 译者简介 | 作者序 | 译者序 |

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内容简介
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N阶算法复杂度的近似快速傅里叶变换(FFT)算法给出小波的应用实例。

● 包含其他小波文献的附加指南。

● 附录中包含Matlab程序。

本书阐述了如何在信号处理、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。本书给出经典信号处理问题的最新观点，特别强调从应用角度出发的信号压缩，涉及当前研究的最新成果。

本书可作为高年级本科生和研究生的教材，适用于信号处理、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。

目录
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前言
Introduction to Wavelets
1.1  Wavelets and Wavelet Expansion Systems
What is a Wavelet Expansion or a Wavelet Transform?
What is a Wavelet System?
More Specific Characteristics of Wavelet Systems
Haar Scaling Functions and Wavelets
What do Wavelets Look Like?
Why is Wavelet Analysis Effective?
1.2  The Discrete Wavelet Transform
1.3  The Discrete-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
Multiresolution Analysis
2.3  The Wavelet Functions
2.4  The Discrete Wavelet Transform
2.5  A Parseval'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 System
Filter Banks and the Discrete Wavelet Transform
3.1  Analysis  From Fine Scale to Coarse Scale Filtering and Down-Sampling or Decimating
3.2  Synthesis - From Coarse Scale to Fine Scale Filtering and Up-Sampling or Stretching
3.3  Input Coefficients
3.4  Lattices and Lifting
3.5  Different Points of View
Multiresolution versus Time-Frequency Analysis
Periodic versus Nonperiodic Discrete Wavelet Transforms
The Discrete Wavelet Transform versus the Discrete-Time Wavelet Transform
Numerical Complexity of the Discrete Wavelet Transform
Bases, Orthogonal Bases, Biorthogonal Bases, Frames, Tight Frames, and Un-conditional Bases
4.1  Bases, Orthogonal Bases, and Biorthogonal Bases
Matrix Examples
Fourier Series Example
Sinc Expansion Example
4.2  Frames and Tight Frames
Matrix Examples
Sinc Expansion as a Tight Frame Example
4.3  Conditional and Unconditional Bases
The Scaling Function and Scaling Coefficients, Wavelet and Wavelet Coeffi-cients
5.1  Tools and Definitions
Signal Classes
Fourier Transforms
Refinement and Transition Matrices
5.2  Necessary Conditions
5.3  Frequency Domain Necessary Conditions
5.4  Sufficient Conditions
Wavelet System Design
5.5  The Wavelet
5.6  Alternate Normalizations
5.7  Example Scaling Functions and Wavelets
Haar Wavelets
Sinc Wavelets
Spline and Battle-Lemarie Wavelet Systems
5.8  Further Properties of the Scaling Function and Wavelet
General Properties not Requiring Orthogonality
Properties that Depend on Orthogonality
5.9  Parameterization of the Scaling Coefficients
Length-2 Scaling Coefficient Vector
Length-4 Scaling Coefficient Vector
Length-6 Scaling Coefficient Vector
5.10 Calculating the Basic Scaling Function and Wavelet
Successive Approximations or the Cascade Algorithm
Iterating the Filter Bank
Successive approximations in the frequency domain
The Dyadic Expansion of the Scaling Function
6  Regularity, Moments, and Wavelet System Design
6.1  K-Regular Scaling Filters
6.2  Vanishing Wavelet Moments
6.3  Daubechies' Method for Zero Wavelet Moment Design
6.4  Non-Maximal Regularity Wavelet Design
6.5  Relation of Zero Wavelet Moments to Smoothness
6.6  Vanishing Scaling Function Moments
6.7  Approximation of Signals by Scaling Function Projection
6.8  Approximation of Scaling Coefficients by Samples of the Signal
6.9  Coifiets and Related Wavelet Systems
Generalized Coifman Wavelet Systems
6.10 Minimization of Moments Rather than Zero Moments
Generalizations of the Basic Uultiresolution Wavelet System
7.1  Tiling the Time-Frequency or Time-Scale Plane
Nonstationary Signal Analysis
Tiling with the Discrete-Time Short-Time Fourier Transform
Tiling with the Discrete Two-Band Wavelet Transform
General Tiling
7.2  Multiplicity-M (M-Band) Scaling Functions and Wavelets
Properties of M-Band Wavelet Systems
M-Band Scaling Function Design
M-Band Wavelet Design and Cosine Modulated Methods
7.3  Wavelet Packets
Full Wavelet Packet Decomposition
Adaptive Wavelet Packet Systems
7.4  Biorthogonal Wavelet Systems
Two-Channel Biorthogonal Filter Banks
Biorthogonal Wavelets
Comparisons of Orthogonal and Biorthogonal Wavelets
Example Families of Biorthogonal Systems
Cohen-Daubechies-Feauveau Family of Biorthogonal Spline Wavelets
Cohen-Daubechies-Feauveau Family of Biorthogonal Wavelets with Less Dissimilar
Filter Length
Tian-Wells Family of Biorthogonal Coifiets
Lifting Construction of Biorthogonal Systems
7.5  Multiwavelets
Construction of Two-Band Multiwavelets
Properties of Multiwavelets
Approximation, Regularity and Smoothness
Support
Orthogonality
Implementation of Multiwavelet Transform
Examples
Geronimo-Hardin-Massopust Multiwavelets
Spline Multiwavelets
Other Constructions
Applications
7.6  Overcomptete Representations, Frames, Redundant Transforms, and Adaptive Bases
Overcomplete Representations
A Matrix Example
Shift-Invariant Redundant Wavelet Transforms and Nondecimated Filter Banks
Adaptive Construction of Frames and Bases
7.7  Local Trigonometric Bases
Nonsmooth Local Trigonometric Bases
Construction of Smooth Windows
Folding and Unfolding
Local Cosine and Sine Bases
Signal Adaptive Local Trigonometric Bases
7.8  Discrete Multiresolution Analysis, the Discrete-Time Wavelet
Transform, and the Continuous Wavelet Transform
Discrete Multiresolution Analysis and the Discrete-Time Wavelet Transform
Continuous Wavelet Transforms
Analogies between Fourier Systems and Wavelet Systems
8  Filter Banks and Transmultiplexers
8.1  Introduction
The Filter Bank
Transmultiplexer
Perfect Reconstruction--A Closer Look
Direct Characterization of PR
Matrix characterization of PR
Polyphase (Transform-Domain) Characterization of PR
8.2  Unitary Filter Banks
8.3  Unitary Filter Banks--Some Illustrative Examples
8.4  M-band Wavelet Tight Frames
8.5  Modulated Filter Banks
Unitary Modulated Filter Bank
8.6  Modulated Wavelet Tight Frames
8.7  Linear Phase Filter Banks
Characterization of Unitary Hp(z) -- PS Symmetry
Characterization of Unitary Hp(z) -- PCS Symmetry
Characterization of Unitary Hp(z) -- Linear-Phase Symmetry
Characterization of Unitary Hp(z) -- Linear Phase and PCS Symmetry
Characterization of Unitary Hp(z) -- Linear Phase and PS Symmetry
8.8  Linear-Phase Wavelet Tight Frames
8.9  Linear-Phase Modulated Filter Banks
DCT/DST I/II based 2M Channel Filter Bank
8.10 Linear Phase Modulated Wavelet Tight Frames
8.11 Time-Varying Filter Bank Trees
Growing a Filter Bank Tree
Pruning a Filter Bank Tree
Wavelet Bases for the Interval
Wavelet Bases for L2([0, ∞])
Wavelet Bases for L2((-∞, 0])
Segmented Time-Varying Wavelet Packet Bases
8.12 Filter Banks and Wavelets--Summary
9  Calculation of the Discrete Wavelet Transform
9.1  Finite Wavelet Expansions and Transforms
9.2  Periodic or Cyclic Discrete Wavelet Transform
9.3  Filter Bank Structures for Calculation of the DWT and Complexity
9.4  The Periodic Case
9.5  Structure of the Periodic Discrete Wavelet Transform
9.6  More General Structures
10  Wavelet-Based Signal Processing and Applications
10.1 Wavelet-Based Signal Processing
10.2 Approximate FFT using the Discrete Wavelet Transform
Introduction
Review of the Discrete Fourier Transform and FFT
Review of the Discrete Wavelet Transform
The Algorithm Development
Computational Complexity
Fast Approximate Fourier Transform
Computational Complexity
Noise Reduction Capacity
Summary
10.3 Nonlinear Filtering or Denoising with the DWT
Denoising by Thresholding
Shift-Invariant or Nondecimated Discrete Wavelet Transform
Combining the Shensa-Beylkin-Mallat-a trous Algorithms and Wavelet Denoising
Performance Analysis
Examples of Denoising
10.4 Statistical Estimation
10.5 Signal and Image Compression
Fundamentals of Data Compression
Prototype Transform Coder
Improved Wavelet Based Compression Algorithms
10.6 Why are Wavelets so Useful?
10.7 Applications
Numerical Solutions to Partial Differential Equations
Seismic and Geophysical Signal Processing
Medical and Biomedical Signal and Image Processing
Application in Communications
Fractals
10.8 Wavelet Software
11 Summary Overview
11.1 Properties of the Basic Multiresolution Scaling Function
11.2 Types of Wavelet Systems
12 References
Bibliography
Appendix A. Derivations for Chapter 5 on Scaling Functions
Appendix B. Derivations for Section on Properties
Appendix C. Matlab Programs
Index

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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。

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