小波导论

所属分类:数学  
出版时间:2009-2   出版时间:人民邮电出版社   作者:崔锦泰   页数:266  
Tag标签:数学,Mathematics,分析,图灵数学,电子  

前言

  Fourier analysis is an established subject in the core of pure and applied mathematical analysis. Not only are the techniques in this subject of fundamental importance in all areas of science and technology, but both the integral Fourier transform and the Fourier series also have significant physical interpretations. In addition, the computational aspects of the Fourier series are especially attractive, mainly because of the orthogonality property of the seties and of its simple expression in terms of only two functions: sin z andCOS X.  Recently, the subject of "vavelet analysis" has drawn much attention from both mathematicians and engineers Mike. Analogous to Fourier analysis, there are also two important mathematical entities in wavelet analysis: the "integral wavelet transform" and the "vavelet series". The integral wavelet transform is defined to be the convolution with respect to the dilation of the reflection of some function, called a "basic wavelet", while the wavelet series is expressed in terms of a single function, called an ":R-wavelet" (or simply, a wavelet) by means of two very simple operations: binary dilations and integral translations. However., unlike Fourier analysis, the integral wavelet transform with a basic wavelet and the wavelet series in terms of a wavelet are intimately related. In fact, if is chosen to be the "dual" of , then the coefficients of the wavelet series of any square-integrable function f are precisely the values of the integral wavelet transform, evaluated at the dyadic positions in the corresponding binary dilated scale levels. Since the integral wavelet transform of f simultaneously localizes f and its Fourier transform f with the zoom-in and zoom-out capability, and since there are real-time algorithms for obtaining the coefficient sequences of the wavelet series, and for recovering f from these sequences, the list of applications of wavelet analysis seems to be endless. On the other hand, polynomial spline functions are among the simplest functions for both computational and implementational purposes. Hence, they are most attractive for analyzing and constructing wavelets.

内容概要

本书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。本书内容安排由浅入深,算法推导详细,既有理论,又有应用背景。  本书自成体系,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。

作者简介

崔锦泰(Charles K.Chui),国际著名的小波分析专家,IEEE会士,密苏里大学路易分校数学与计算机科学系讲座教授,该校计算调和分析研究所所长,斯坦福大学顾部教授。曾担任数个国际著名期刊和丛书的主编或编委。他在调和分析应用、逼近及其应用等领域也做出了杰出的贡献,首创将样条应用于小波中。

书籍目录

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
Poisson's
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 Waveletcseries 4.cCardinalcSplinecAnalysis  4.1 Cardinalcsplinecspaces  4.2 B-splinescandctheircbasiccpropertiesc 4.3 Thectwo-scalecrelationcandcancinterpolatorycgraphicalcdisplaycalgorithm  4.4 B-netcrepresentationscandccomputationcofccardinalcsplines  4.5 Constructioncofcsplinecapproximationcformulas  4.6 Constructioncofcsplinecinterpolationcformulas5.cScalingcFunctionscandcWavelets 5.1 Multiresolutioncanalysis  5.2 Scalingcfunctionscwithcfinitectwo-scalecrelations  5.3 Direct-sumcdecompositionscofcL2(R)  5.4 Waveletscandctheircduals  5.5 Linear-phasecfiltering  5.6 Compactlycsupportedcwavelets 6.cCardinalcSpline-Wavelets  6.1 Interpolatorycspline-wavelets  6.2 Compactlycsupportedcspline-wavelets  6.3 Computationcofccardinalcspline-wavelets  6.4 EulerFrobeniuspolynomials  6.5 Errorcanalysiscincsplinecwaveletcdecomposition  6.6 Totalcpositivity,ccompletecoscillation,czero-crossings 7.cOrthogonalcWaveletscandcWaveletcPackets  7.1 Examplescofcorthogonalcwavelets  7.2 Identificationcofcorthogonalctwo-scalecsymbols  7.3 Constructioncofccompactlycsupportedcorthogonalcwavelets  7.4 Orthogonalcwaveletcpackets  7.5 Orthogonalcdecompositioncofcwaveletcseries NotesReferences Subject
Index Appendixc

章节摘录

  An
Overview  "Wavelets"
has
been
a
very
popular
topic
of
conversations
in
many
scientific
and
engineering
gatherings
these
days.
Some
view
wavelets
as
a
new
basis
for
representing
functions,
some
consider
it
as
a
technique
for
time-frequency
analysis,
and
others
think
of
it
as
a
new
mathematical
subject.
Of
course,
all
of
them
are
right,
since
"wavelets"
is
a
versatile
tool
with
very
rich
mathematical
content
and
great
potential
for
applications.
However,
as
this
subject
is
still
in
the
midst
of
rapid
development,
it
is
definitely
too
early
to
give
a
unified
presentation.
The
objective
of
this
book
is
very
modest:
it
is
intended
to
be
used
as
a
textbook
for
an
introductory
one-semester
course
on
"wavelet
analysis"
for
upper-division
undergraduate
or
beginning
graduate
mathematics
and
engineering
students,
and
is
also
written
for
both
mathematicians
and
engineers
who
wish
to
learn
about
the
subject.
For
the
specialists,
this
volume
is
suitable
as
complementary
reading
to
the
more
advanced
monographs,
such
as
the
two
volumes
of
Ondelettes
et
Operateurs
by
Yves
Meyer,
the
edited
volume
of
Wavelets-A
Tutorial
in
Theory
and
Applications
in
this
series,
and
the
forthcoming
CBMS
volume
by
Ingrid
Danbechies.  Since
wavelet
analysis
is
a
relatively
new
subject
and
the
approach
and
organization
in
this
book
are
somewhat
different
from
that
in
the
others,
the
goal
of
this
chapter
is
to
convey
a
general
idea
of
what
wavelet
analysis
is
about
and
to
describe
what
this
book
aims
to
cover.  1.1.
From
Fourier
analysis
to
wavelet
analysis

编辑推荐

  《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。

图书封面

图书标签Tags

数学,Mathematics,分析,图灵数学,电子


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用户评论 (总计27条)

 
 

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  •     字体还是很清楚的, 就是有基本上都有些歪斜, 这评论页在火狐下显示不正常, 差点就没评论上, 当当的设计人员还需要补功课
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  •     应该是从PDF打印的,符号不是很清晰
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  •     不过,讨论问题非常细致。
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  •     还可以啊,很好很强大
  •     学习数论的不错的书,挺容易上手
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  •     不错!值得深读,很让人无语。。。。。。。。。。。
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