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BL
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| Record Number
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891074
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| Main Entry
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Farkov, Yu. A.
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| Title & Author
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Construction of wavelets through Walsh functions /\ Yu. A. Farkov, Pammy Manchanda, Abul Hasan Siddiqi.
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| Publication Statement
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Singapore :: Springer,, [2019]
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| Series Statement
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Industrial and applied mathematics
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| Page. NO
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1 online resource
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| ISBN
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9789811363702
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: 9789811363719
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: 9789811363726
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: 9811363706
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: 9811363714
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: 9811363722
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9789811363696
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9811363692
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| Notes
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8 Wavelets Associated with Nonuniform Multiresolution Analysis on Positive Half Line
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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Intro; Preface; References; Contents; About the Authors; Introduction; References; 1 Introduction to Walsh Analysis and Wavelets; 1.1 Walsh Functions; 1.2 Walsh-Fourier Transform; 1.3 Haar Functions and Its Relationship with Walsh Functions; 1.4 Walsh-Type Wavelet Packets; 1.5 Wavelet Analysis; 1.5.1 Continuous Wavelet Transform; 1.5.2 Discrete Wavelet System; 1.5.3 Multiresolution Analysis; 1.6 Wavelets with Compact Support; 1.7 Exercises; References; 2 Walsh-Fourier Series; 2.1 Walsh-Fourier Coefficients; 2.1.1 Estimation of Walsh-Fourier Coefficients
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2.1.2 Transformation of Walsh-Fourier Coefficients2.2 Convergence of Walsh-Fourier Series; 2.2.1 Summability in Homogeneous Banach Spaces; 2.3 Approximation by Transforms of Walsh-Fourier Series; 2.3.1 Approximation by Césaro Means of Walsh-Fourier Series; 2.3.2 Approximation by Nörlund Means of Walsh-Fourier Series in Lp Spaces; 2.3.3 Approximation by Nörlund Means in Dyadic Homogeneous Banach Spaces and Hardy Spaces; 2.4 Applications to Signal and Image Processing; 2.4.1 Image Representation and Transmission; 2.4.2 Data Compression; 2.4.3 Quantization of Walsh Coefficients
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2.4.4 Signal Processing2.4.5 ECG Analysis; 2.4.6 EEG Analysis; 2.4.7 Speech Processing; 2.4.8 Pattern Recognition; 2.5 Exercises; References; 3 Haar-Fourier Analysis; 3.1 Haar System and Its Generalization; 3.2 Haar Fourier Series; 3.3 Haar System as Basis in Function Spaces; 3.4 Non-uniform Haar Wavelets; 3.5 Generalized Haar Wavelets and Frames; 3.6 Applications of Haar Wavelets; 3.6.1 Applications to Solutions of Initial and Boundary Value Problems; 3.6.2 Applications to Solutions of Integral Equations; 3.7 Exercises; References
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4 Construction of Dyadic Wavelets and Frames Through Walsh Functions4.1 Preliminary; 4.2 Orthogonal Wavelets and MRA in L2(mathbbR+); 4.3 Orthogonal Wavelets with Compact Support on mathbbR+; 4.4 Estimates of the Smoothness of the Scaling Functions; 4.5 Approximation Properties of Dyadic Wavelets; 4.6 Exercise; References; 5 Orthogonal and Periodic Wavelets on Vilenkin Groups; 5.1 Multiresolution Analysis on Vilenkin Groups; 5.2 Compactly Supported Orthogonal p-Wavelets; 5.3 Periodic Wavelets on Vilenkin Groups; 5.4 Periodic Wavelets Related to the Vilenkin-Christenson Transform
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5.5 Application to the Coding of Fractal FunctionsReferences; 6 Haar-Vilenkin Wavelet; 6.1 Introduction; 6.2 Haar-Vilenkin Wavelets; 6.2.1 Haar-Vilenkin Mother Wavelet; 6.3 Approximation by Haar-Vilenkin Wavelets; 6.4 Covergence Theorems; 6.5 Haar-Vilenkin Coefficients; 6.6 Exercises; References; 7 Construction Biorthogonal Wavelets and Frames; 7.1 Biorthogonal Wavelets on R+; 7.2 Biorthogonal Wavelets on Vilenkin Groups; 7.3 Construction of Biorthogonal Wavelets on The Vilenkin Group; 7.4 Frames on Vilenkin Group; 7.5 Application to Image Processing; References
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| Abstract
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This book focuses on the fusion of wavelets and Walsh analysis, which involves non-trigonometric function series (or Walsh-Fourier series). The primary objective of the book is to systematically present the basic properties of non-trigonometric orthonormal systems such as the Haar system, Haar-Vilenkin system, Walsh system, wavelet system and frame system, as well as updated results on the book's main theme. Based on lectures that the authors presented at several international conferences, the notions and concepts introduced in this interdisciplinary book can be applied to any situation where wavelets and their variants are used. Most of the applications of wavelet analysis and Walsh analysis can be tried for newly constructed wavelets. Given its breadth of coverage, the book offers a valuable resource for theoreticians and those applying mathematics in diverse areas. It is especially intended for graduate students of mathematics and engineering and researchers interested in applied analysis.
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| Subject
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Walsh functions.
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| Subject
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Wavelets (Mathematics)
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| Subject
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Walsh functions.
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| Subject
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Wavelets (Mathematics)
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| Dewey Classification
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515/.2433
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| LC Classification
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QA403.3.F37 2019
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| Added Entry
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Manchanda, P., (Pammy)
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Siddiqi, A. H.
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