Wavelet transforms kith and kin
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.
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| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
Boca Raton, London, New York
CRC Press
2023
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| Ausgabe: | First edition |
| Schriftenreihe: | Textbooks in mathematics
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| Online Zugang: | Inhaltsverzeichnis |
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Tag hinzufügen | Zusammenfassung: | 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. 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 -- 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 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 -- 2.4. The Windowed Linear Canonical Transform -- 2.4.1. Definition and basic properties. |
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| Beschreibung: | Literaturverzeichnis: Seite 457-475 |
| Beschreibung: | xxi, 479 Seiten Diagramme |
| ISBN: | 9781032007960 978-1-032-00796-0 9781032344959 978-1-032-34495-9 |