Wavelet transforms : kith and kin /: kith and kin. (2022)

• Record Type: Book
• Further Information: Note: Firdous A. Shah, Azhar Y. Tantary.
• Authors: Shah, Firdous Ahmad; Tantary, Azhar Y
• Contents: List of Figures xix 1 The Fourier Transforms 1; 1.1 Introduction; 1.2 The Fourier Transform; 1.2.1 Definition and Examples; 1.2.2 Basic Properties of the Fourier Transform; 1.2.3 Convolution and Correlation; 1.2.4 Shannon’s Sampling Theorem; 1.2.5 Uncertainty Principle for the Fourier Transform; 1.3 The Fractional Fourier Transform; 1.3.1 Definition and Basic Properties; 1.3.2 Fractional Convolution and Correlation; 1.3.3 Uncertainty Principle for the Fractional Fourier Transform; 1.4 The Linear Canonical Transform; 1.4.1 Definition and Basic Properties; 1.4.2 Linear Canonical Convolution and Correlation; 1.4.3 Applications of Linear Canonical Transform to Differential Equations; 1.4.4 Uncertainty Principle for the Linear Canonical Transform; 1.5 The Special Affine Fourier Transform; 1.5.1 Definition and Basic Properties; 1.5.2 Special Affine Convolution and Correlation; 1.6 The Quadratic-phase Fourier Transform; 1.6.1 Definition and Basic Properties; 1.6.2 Quadratic-phase Convolution and Correlation; 1.6.3 Applications of Quadratic-phase Fourier Transform; 1.7 The Two-dimensional Fourier Transform; 1.8 Exercises 2 The Windowed Fourier Transforms 119; 2.1 Introduction; 2.2 The Windowed Fourier Transform; 2.2.1 Analysis of Window Functions; 2.2.2 Definition and Basic Properties; 2.2.3 Time-Frequency Resolution and Uncertainty Principles; 2.3 The Windowed Fractional Fourier Transform; 2.3.1 Definition and Basic Properties; 2.3.2 Time-Fractional-Frequency Resolution; 2.4 The Windowed Linear Canonical Transform; 2.4.1 Definition and Basic Properties; 2.4.2 Resolution of Windowed Linear Canonical Transform and Uncertainty; Principle; 2.5 The Windowed Special Affine Fourier Transform; 2.6 The Windowed Quadratic-Phase Fourier Transform; 2.7 The Directional Windowed Fourier Transform; 2.8 Exercises 3 The Wavelet Transforms and Kin 193; 3.1 Introduction; 3.2 The Wavelet Transform; 3.2.1 Wavelet Transform: A Group Theoretical Approach; 3.2.2 Wavelet Transform: An Analytical Perspective; 3.3 The Stockwell Transform; 3.3.1 Definition and Basic Properties; 3.4 The Two-dimensional Wavelet Transform; 3.4.1 Two-dimensional Wavelet Transform: A Group Theoretic Approach; 3.4.2 Two-dimensional Wavelet Transform: An Analytical Perspective; 3.4.3 Different Classes of Two-dimensional Wavelets; 3.4.4 Representation Classes and Energy Densities for Two-dimensional; Wavelet Transform; 3.5 The Ridgelet Transform; 3.5.1 Radon Transform; 3.5.2 Ridgelet Transform: Definition and Basic Properties; 3.6 The Curvelet and Ripplet Transforms; 3.6.1 Curvelet Transform; 3.6.2 Ripplet Transform; 3.7 The Shearlet Transforms; 3.7.1 Shearlet Transform: A Group Theoretical Approach; 3.7.2 Shearlet Transform: An Analytical Perspective; 3.7.3 Visualization of the Shearlet Coefficients; 3.7.4 Cone-adapted Shearlet Transform; 3.8 The Bendlet Transform; 3.8.1 Definition and Basic Properties; 3.8.2 Applications of Bendlet Transform to Partial Differential Equations; 3.9 Exercises 4 The Intertwining of Wavelet Transforms; 4.1 Introduction; 4.2 The Fractional Wavelet Transform; 4.2.1 Definition and Basic Properties; 4.2.2 Constant Q-Property and Time-Fractional-Frequency Resolution; 4.3 The Fractional Stockwell Transform; 4.3.1 Definition and Basic Properties; 4.4 The Linear Canonical Wavelet Transform; 4.4.1 Convolution-based Linear Canonical Wavelet Transform 4.4.2 Constant Q-Property and Resolution of the Convolution-based Linear Canonical Wavelet Transform; 4.4.3 Composition of Linear Canonical Wavelet Transforms; 4.4.4 Modified Linear Canonical Wavelet Transform; 4.5 The Linear Canonical Stockwell Transform; 4.5.1 Definition and Basic Properties; 4.6 The Linear Canonical Ridgelet Transform; 4.6.1 Definition and Basic Properties ; 4.7 The Linear Canonical Curvelet and Ripplet Transforms; 4.7.1 Linear Canonical Curvelet Transform; 4.7.2 Linear Canonical Ripplet Transform; 4.8 The Linear Canonical Shearlet Transform; 4.8.1 Definition and Basic Properties; 4.8.2 Uncertainty Principle for the Linear Canonical Shearlet Transform; 4.9 Exercises 5 The Wavelet Transforms and Kith 413; 5.1 Introduction; 5.2 The Laguerre Wavelet Transform; 5.2.1 Laguerre Polynomials and Transform; 5.2.2 Laguerre Wavelet Transform: Definition and Basic Properties; 5.3 The Legendre Wavelet Transform; 5.3.1 Legendre Polynomials and Transform; 5.3.2 Legendre Wavelet Transform: Definition and Basic Properties; 5.4 The Bessel Wavelet Transform; 5.4.1 Bessel Functions and Hankel Transform; 5.4.2 Bessel Wavelet Transform: Definition and Basic Properties; 5.5 The Dunkl Wavelet Transform; 5.5.1 Dunkl Transform; 5.5.2 Dunkl Wavelet Transform: Definition and Basic Properties; 5.6 The Mehler-Fock Wavelet Transform; 5.6.1 Mehler-Fock Transform; 5.6.2 Mehler-Fock Wavelet Transform: Definition and Basic Properties; 5.7 The Interface of Wavelet and Hartley Transforms; 5.7.1 Hartley Transform; 5.7.2 Hartley-based Wavelet Transform; 5.8 Exercises Bibliography 457 Index 475;
• Edition: 1st
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2022
• Extent: 1 online resource, illustrations (colour)
• Subjects: 515.2433; Wavelets (Mathematics); Time-series analysis
• Languages: English
• ISBNs: 9781000771633; 9781000771619; 9781003175766
• Related ISBNs: 9781032007960
• Notes: Note: Includes bibliographical references and index.; Note: Description based on CIP data; resource not viewed.
• 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.