A First Course in Wavelets with Fourier Analysis, 2nd EditionISBN: 978-0-470-43117-7
Hardcover
336 pages
September 2009
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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 in Wavelets with Fourier Analysis, 2nd Edition (US $116.00)
-and- Discrete Wavelet Transformations: An Elementary Approach with Applications (US $142.00)
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