A first course in wavelets with Fourier analysis
A comprehensive, self-contained treatment of Fourier analysis and wavelets-now in a new edition Through expansive coverage and easy-to-follow explanations, A First Course in Wavelets with Fourier Analysis, Second Edition provides a self-contained mathematical treatment of Fourier analysis and wavele...
| Otros Autores: | , |
|---|---|
| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
Hoboken, New Jersey :
Wiley
2009.
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| Edición: | 2nd ed |
| Materias: | |
| Ver en Biblioteca Universitat Ramon Llull: | https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009849109306719 |
Tabla de Contenidos:
- Cover; Title Page; Copyright; PREFACE AND OVERVIEW; 0: INNER PRODUCT SPACES; 0.1 MOTIVATION; 0.2 DEFINITION OF INNER PRODUCT; 0.3 THE SPACES L2 AND L2; 0.4 SCHWARZ AND TRIANGLE INEQUALITIES; 0.5 ORTHOGONALITY; 0.6 LINEAR OPERATORS AND THEIR ADJOINTS; 0.7 LEAST SQUARES AND LINEAR PREDICTIVE CODING; EXERCISES; 1: FOURIER SERIES; 1.1 INTRODUCTION; 1.2 COMPUTATION OF FOURIER SERIES; 1.3 CONVERGENCE THEOREMS FOR FOURIER SERIES; EXERCISES; 2: THE FOURIER TRANSFORM; 2.1 INFORMAL DEVELOPMENT OF THE FOURIER TRANSFORM; 2.2 PROPERTIES OF THE FOURIER TRANSFORM; 2.3 LINEAR FILTERS
- 2.4 THE SAMPLING THEOREM2.5 THE UNCERTAINTY PRINCIPLE; EXERCISES; 3: DISCRETE FOURIER ANALYSIS; 3.1 THE DISCRETE FOURIER TRANSFORM; 3.2 DISCRETE SIGNALS; 3.3 DISCRETE SIGNALS & MATLAB; EXERCISES; 4: HAAR WAVELET ANALYSIS; 4.1 WHY WAVELETS?; 4.2 HAAR WAVELETS; 4.3 HAAR DECOMPOSITION AND RECONSTRUCTION ALGORITHMS; 4.4 SUMMARY; EXERCISES; 5: MULTIRESOLUTION ANALYSIS; 5.1 THE MULTIRESOLUTION FRAMEWORK; 5.2 IMPLEMENTING DECOMPOSITION AND RECONSTRUCTION; 5.3 FOURIER TRANSFORM CRITERIA; EXERCISES; 6: THE DAUBECHIES WAVELETS; 6.1 DAUBECHIES' CONSTRUCTION; 6.2 CLASSIFICATION, MOMENTS, AND SMOOTHNESS
- 6.3 COMPUTATIONAL ISSUES6.4 THE SCALING FUNCTION AT DYADIC POINTS; EXERCISES; 7: OTHER WAVELET TOPICS; 7.1 COMPUTATIONAL COMPLEXITY; 7.2 WAVELETS IN HIGHER DIMENSIONS; 7.3 RELATING DECOMPOSITION AND RECONSTRUCTION; 7.4 WAVELET TRANSFORM; APPENDIX A: TECHNICAL MATTERS; APPENDIX B: SOLUTIONSTOSELECTED EXERCISES; APPENDIX C: MATLAB® ROUTINES; BIBLIOGRAPHY; INDEX
