A first course in wavelets with Fourier analysis = 小波与傅里叶分析基础 /
副标题：无
作 者：Albert Boggess, Francis J. Narcowich 著.
分类号：O174.22
ISBN：9787505376601
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简介
自19世纪以来，关于傅里叶系列和傅里叶变换的许多研究文件和书籍已有很多。相比之下，小波的发展则是近来才出现的事情，尽管其发展可追溯到几十年前，但小波应用于信息分析和其他应用领域则是近二十年的事情。本书的目的主要是向读者展示傅里叶分析和小波的许多基础知识以及在信号分析方面的应用。全书分为8章和2个附录，前言部分是学习第1章至第7章的准备知识，即内积空间；第1章讲解傅里叶级数的基础知识；第2章讲解傅里叶变换；第3章介绍离散傅里叶变换以及快速傅里叶变换；第4章~第7章讨论小波，重点在于正交小波的构建；附录部分则介绍稍微复杂的一些技术主题以及演示概念或产生图形的MATLAB代码。许多关于小波的文章和参考书籍均要求读者具有复杂的数学背景知识，本书则只要求学生具有较好的微积分知识以及线性代数知识，通俗易懂。
目录
0 inner product spaces
0.1 motivation
0.2 definition of inner product
0.3 the spaces l2 and l2
0.4 schwarz and triangle inequalitiea
0.5 orthogonality
0.6 linear operators and their adjoints
0.7 least squares and linear predictive coding
0.8 exercises
1 fourier series
1.1 tntroduction
1.2 computation of fourier series
1.3 oonvergence theorems for fourier series
1.4 exercises
2 the fourier transform
2.1 informal development of the fourier transform
2.2 properties of the fourier transform
2.3 linear filters
2.4 the sampling theorem
2.5 the uncertainty principle
. 2.6 exercises
3 discrete fourier analysis
3.1 the discrete fourier transform
3.2 discrete signals
3.3 exercises
4 haar wavelet analysis
4.1 why wavelet.s?
4.2 haar wavelets
4.3 haar decomposition and reconstruction algorithms
4.4 summary
4. 5 exercises
5 multiresolution analysis
5.1 the multiresolution framework
5.2 implementing decomposition and reconstruction
5.5 fourier t$ansform criteria
5.4 exercises
6 the daubechies wavelets
6.1 daubechies's construction
6.2 olassification, bvloments, and smoothness
6.3 computational issues
6.4 the scaling function at dyadic points
6.5 exercises
7 other wavelet topics
7.1 oomputational complexity
7.2 wavelets in higher dimensions
7.3 relating decomposition and reconstruction
7.4 wavelet transform
appendix a technical matters
a.1 proof of the fourier inversion formula
a.2 rigoroue proof of theorem 5.17
appendix b matlab routines
b.1 general compression routine
b.2 use of matlan's fft routine for filtering ailcl compression
b.3 sample routines using matlan's wavelet toolbox
b.4 matlan code for the algorithms in section 5.2
bibliography
index
0.1 motivation
0.2 definition of inner product
0.3 the spaces l2 and l2
0.4 schwarz and triangle inequalitiea
0.5 orthogonality
0.6 linear operators and their adjoints
0.7 least squares and linear predictive coding
0.8 exercises
1 fourier series
1.1 tntroduction
1.2 computation of fourier series
1.3 oonvergence theorems for fourier series
1.4 exercises
2 the fourier transform
2.1 informal development of the fourier transform
2.2 properties of the fourier transform
2.3 linear filters
2.4 the sampling theorem
2.5 the uncertainty principle
. 2.6 exercises
3 discrete fourier analysis
3.1 the discrete fourier transform
3.2 discrete signals
3.3 exercises
4 haar wavelet analysis
4.1 why wavelet.s?
4.2 haar wavelets
4.3 haar decomposition and reconstruction algorithms
4.4 summary
4. 5 exercises
5 multiresolution analysis
5.1 the multiresolution framework
5.2 implementing decomposition and reconstruction
5.5 fourier t$ansform criteria
5.4 exercises
6 the daubechies wavelets
6.1 daubechies's construction
6.2 olassification, bvloments, and smoothness
6.3 computational issues
6.4 the scaling function at dyadic points
6.5 exercises
7 other wavelet topics
7.1 oomputational complexity
7.2 wavelets in higher dimensions
7.3 relating decomposition and reconstruction
7.4 wavelet transform
appendix a technical matters
a.1 proof of the fourier inversion formula
a.2 rigoroue proof of theorem 5.17
appendix b matlab routines
b.1 general compression routine
b.2 use of matlan's fft routine for filtering ailcl compression
b.3 sample routines using matlan's wavelet toolbox
b.4 matlan code for the algorithms in section 5.2
bibliography
index
A first course in wavelets with Fourier analysis = 小波与傅里叶分析基础 /
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