小波分析導(dǎo)論

內(nèi)容概要

　  《小波分析導(dǎo)論》是關(guān)于小波分析的一本導(dǎo)論性專題著作，著重于樣條一小波和時-頻分析．它包括的基本內(nèi)容是：小波級數(shù)，多分辨分析、小波分解與重構(gòu)，Cabor變換與短時Fourier變換、時頻局部化、積分小波變換、二進(jìn)小波、框架、樣條-小波、標(biāo)準(zhǔn)正交小波基和小波包．另外，對非正交、半正交和正交小波提出了統(tǒng)一的論述．該書內(nèi)容豐富，取材精煉、重點突出、敘述清楚．內(nèi)容安排由淺入深，算法推導(dǎo)詳細(xì)，既有理論，又有應(yīng)有背景?！? 《小波分析導(dǎo)論》是自我包容的，只要求大學(xué)理工科各專業(yè)具有函數(shù)理論和實分析的基本知識即可．它既適合作為理工科大學(xué)學(xué)生學(xué)習(xí)小波分析的入門教程，也適合作為希望學(xué)習(xí)這個課題的科技工作者的指導(dǎo)讀物．有關(guān)專家借助此書，可以更好地閱讀在該領(lǐng)域中已經(jīng)發(fā)表的大量的文獻(xiàn)。

作者簡介

作者：(美國)瓦爾納(David F.Walnut)

書籍目錄

Ⅰ Preliminaries1 Functions and Convergence1.1 Functions1.1.1 Bounded Functions1.1.2 Integrable Functions1.1.3 Square Integrable Functions1.1 .4 Differentiable Functions1.2 Convergence of Sequences of Functions1.2.1 Numerical Convergence1.2.2 Pointwise Convergence1.2.3 Uniform Convergence1.2.4 Mean Convergence1.2.5 Mean square Convergence1.2.6 Interchange of Limits and Integrals2 Fourier Series2.1 Trigonometric Series2.1.1 Periodic Functions2.1.2 The Trigonometric System2.1.3 The Fourier Coefficients2.1.4 Convergence of Fourier Series2.2 Approximate Identities2.2.1 Motivation from Fourier Series2.2.2 Definition and Examples2.2.3 Convergence Theorems2.3 Generalized Fourier Series2.3.1 0rthogonality2.3.2 Generalized Fourier Series2.3.3 Completeness3 The Fourier Transform3.1 Motivation and Definition3.2 Basic Properties ofthe Fourier Transform3.3 Fourier Inversion3.4 Convolution3.5 Plancherers Formula3.6 The Fourier Transform for L2 Functions3.7 Smoothness versus Decay3.8 Dilation, Translation, and Modulation3.9 Bandlimited Functions and the Sampling Formula4.Signals and Systems4.1 Signals4.2 Systems4.2.1 Causality and Stability4.3 Periodic Signals and the Discrete Fourier Transform4.3.1 The Discrete Fourier Transform4.4 The Fast Fourier Transform4.5 L2 Fourier SeriesⅡ The Haar System5 The Haar System5.1 Dyadic Step Functions5.1.1 The Dyadic Intervals5.1.2 The Scale j Dyadic Step Functions5.2 The Haar System5.2.1 The Haar Scaling Functions and the Haar Functions5.2.2 Orthogonality of the Haar System5.2.3 The Splitting Lemma5.3 Haar Bases on [0, 1]5.4 Comparison of Haar Series with Fourier Series5.4.1 Representation of Functions with Small Support 5.4.2 Behavior of Haar Coefficients Near Jump Discontinuities5.4.3 Haar Coefficients and Global Smoothness5.5 Haar Bases on R5.5.1 The Approximation and Detail Operators5.5.2 The Scale J Haar System on R5.5.3 The Haar System on R6 The Discrete Haar Transform6.1 Motivation6.1.1 The Discrete Haar Transform （DHT）6.2 The DHT in Two Dimensions6.2.1 The Row-wise and Column-wise Approximations and Details……Ⅲ Orthonormal Wavelet BasesⅣ Other Wavelet ConstructionsⅤ ApplicationsⅥ AppendixesIndex

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