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by Francis J. Narcowich, Albert Boggess
A First Course in Wavelets with Fourier Analysis, 2nd Edition
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Title Page
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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 THEOREM
2.5 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 ISSUES
6.4 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: SOLUTIONS TO SELECTED EXERCISES
APPENDIX C: MATLAB® ROUTINES
BIBLIOGRAPHY
INDEX
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A First Course inWavelets with Fourier Analysis
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