Fundamentals of wavelets /
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| Format: | eBook |
| Language: | English |
| Published: |
Southampton ; Boston :
WIT Press : Science Press,
[2012]
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| Series: | Chinese science today.
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| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- Cover; Fundamentals of Wavelets; Copyright Page; Preface; Contents; 1. Mathematical preliminaries; 1.1 Some mathematical concepts and knowledge; 1.2 Fourier series; 1.3 Fourier transforms; 1.4 Sampling theorem and filtering; 2. Wavelet transform and its applications; 2.1 Wavelet transforms; 2.2 Applications of wavelet transforms; 3. Multiresolution and orthogonal wavelets; 3.1 Multiresolution analysis; 3.2 Filter response functions and their applications; 3.3 Effects of filters - Mallat algorithms; 3.4 Reconstruction algorithms; 3.5 Regularity and vanishing moments of wavelets; 3.6 Wavelets are telescopes and microscopes in mathematics4. Compactly supported real wavelets; 4.1 Some relative questions; 4.2 Constructions of compactly supported wavelets; 4.3 Decomposition and reconstruction algorithms; 5. Wavelet packet analysis; 5.1 Wavelet packet decompositions; 5.2 Choices of the best wavelet packet bases; 5.3 Algorithms; 6. Multivariate wavelets; 6.1 Principles of multivariate wavelets to deal with problems; 6.2 Bivariate multiresolution analysis; 6.3 Mallat algorithms; 6.4 Sampling algorithms; 7. Biorthogonal wavelets; 7.1 Constructions and algorithms; 7.2 Compactly supported biorthogonal real wavelets8. Spline wavelets; 8.1 Simple introductions of splines; 8.2 Constructions of spline wavelets; 9. The lifting theory of biorthogonal wavelets; 9.1 Principles of the lifting theory of biorthogonal wavelets; 9.2 Algorithms of lifted biorthogonal wavelets; 9.3 Examples of choices of lifting filters; 9.4 A direct method to construct biorthogonal wavelets; Bibliography;