小波分析导论
2011-7
世界图书出版公司
瓦尔纳
449
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《小波分析导论》是关于小波分析的一本导论性专题著作，着重于样条一小波和时-频分析．它包括的基本内容是：小波级数，多分辨分析、小波分解与重构，Cabor变换与短时Fourier变换、时频局部化、积分小波变换、二进小波、框架、样条-小波、标准正交小波基和小波包．另外，对非正交、半正交和正交小波提出了统一的论述．该书内容丰富，取材精炼、重点突出、叙述清楚．内容安排由浅入深，算法推导详细，既有理论，又有应有背景。 《小波分析导论》是自我包容的，只要求大学理工科各专业具有函数理论和实分析的基本知识即可．它既适合作为理工科大学学生学习小波分析的入门教程，也适合作为希望学习这个课题的科技工作者的指导读物．有关专家借助此书，可以更好地阅读在该领域中已经发表的大量的文献。
作者：(美国)瓦尔纳(David F.Walnut)
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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《小波分析导论(英文版)》由世界图书出版公司出版。
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很经典，老师推荐的！