Wavelets and Wavelet Transforms by C. Sidney Burrus - HTML preview
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Wavelets and Wavelet Transforms
Table of Contents
- Chapter 1. Preface
- Chapter 2. Introduction to Wavelets
- Chapter 3. A multiresolution formulation of Wavelet Systems
- Chapter 4. Filter Banks and the Discrete Wavelet Transform
- Chapter 5. Bases, Orthogonal Bases, Biorthogonal Bases, Frames, Tight Frames, and unconditional Bases
- Chapter 6. The Scaling Function and Scaling Coefficients, Wavelet and Wavelet Coefficients
- 6.1. Tools and Definitions
- 6.2. Necessary Conditions
- 6.3. Frequency Domain Necessary Conditions
- 6.4. Sufficient Conditions
- 6.5. The Wavelet
- 6.6. Alternate Normalizations
- 6.7. Example Scaling Functions and Wavelets
- 6.8. Further Properties of the Scaling Function and Wavelet
- 6.9. Parameterization of the Scaling Coefficients
- 6.10. Calculating the Basic Scaling Function and Wavelet
- 6.11. References
- Chapter 7. Regularity, Moments, and Wavelet System Design
- 7.1. K-Regular Scaling Filters
- 7.2. Vanishing Wavelet Moments
- 7.3. Daubechies' Method for Zero Wavelet Moment Design
- 7.4. Non-Maximal Regularity Wavelet Design
- 7.5. Relation of Zero Wavelet Moments to Smoothness
- 7.6. Vanishing Scaling Function Moments
- 7.7. Approximation of Signals by Scaling Function Projection
- 7.8. Approximation of Scaling Coefficients by Samples of the Signal
- 7.9. Coiflets and Related Wavelet Systems
- 7.10. Minimization of Moments Rather than Zero Moments
- 7.11. References
- Chapter 8. Generalizations of the Basic Multiresolution Wavelet System
- 8.1. Tiling the Time–Frequency or Time–Scale Plane
- 8.2. Multiplicity-M (M-Band) Scaling Functions and Wavelets
- 8.3. Wavelet Packets
- 8.4. Biorthogonal Wavelet Systems
- Two Channel Biorthogonal Filter Banks
- Biorthogonal Wavelets
- Comparisons of Orthogonal and Biorthogonal Wavelets
- Example Families of Biorthogonal Systems
- Cohen-Daubechies-Feauveau Family of Biorthogonal Spline Wavelets
- Cohen-Daubechies-Feauveau Family of Biorthogonal Wavelets with Less Dissimilar Filter Length
- Tian-Wells Family of Biorthogonal Coiflets
- Lifting Construction of Biorthogonal Systems
- 8.5. Multiwavelets
- 8.6. Overcomplete Representations, Frames, Redundant Transforms, and Adaptive Bases
- 8.7. Local Trigonometric Bases
- 8.8. Discrete Multiresolution Analysis, the Discrete-Time Wavelet Transform, and the Continuous Wavelet Transform
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