| Description |
1 online resource (502 p.) |
| Series |
Textbooks in Mathematics Ser |
|
Textbooks in Mathematics Ser
|
| Contents |
Cover -- Half Title -- Series Page -- Title Page -- Copyright Page -- Dedication -- Contents -- Foreword by Prof. Srivastava -- Foreword by Prof. Jorgensen -- Preface -- List of Figures -- 1. The Fourier Transforms -- 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 |
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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 |
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1.6.1. Definition and basic properties -- 1.6.2. Quadratic-phase convolution and correlation -- 1.6.3. Applications of the quadratic-phase Fourier transform -- 1.7. The Two-Dimensional Fourier Transform -- 1.8. Exercises -- 2. The Windowed Fourier Transforms -- 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 |
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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 -- 3.1. Introduction -- 3.2. The Wavelet Transform -- 3.2.1. Wavelet transform: A group theoretic approach -- 3.2.2. Wavelet transform: An analytical perspective -- 3.3. The Stockwell Transform |
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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 partial energy densities of 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 |
| Summary |
This textbook serves as an introduction to contemporary aspects of time-frequency analysis encompassing the theory of Fourier transforms, wavelet transforms and their respective off-shoots |
| Notes |
Description based upon print version of record |
|
3.7. The Shearlet Transforms |
| Subject |
Wavelets (Mathematics)
|
|
Wavelets (Mathematics)
|
| Form |
Electronic book
|
| Author |
Tantary, Azhar Y
|
| ISBN |
9781000771633 |
|
1000771636 |
|
9781000771619 |
|
100077161X |
|
9781003175766 |
|
1003175767 |
|
