Construction of wavelets through Walsh functions. ([2019])

• Record Type: Book
• Further Information: Note: Yu. A. Farkov, Pammy Manchanda, Abul Hasan Siddiqi.
• Authors: Farkov, Yu. A; Manchanda, P (Pammy); Siddiqi, A. H
• Contents: 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 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 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 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 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
• Publisher Details: Singapore : Springer
• Publication Date: 2019
• Extent: 1 online resource
• Subjects: 515/.2433; Wavelets (Mathematics); Walsh functions; Electronic books; Electronic books
• Languages: English
• ISBNs: 9789811363702; 9811363706
• Related ISBNs: 9789811363696
• Notes: Note: Includes bibliographical references and index.; Note: Description based on online resource; title from digital title page (viewed on May 17, 2019).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.