Introduction to Wavelets and Wavelet Transforms: A Primer
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TL;DR
This work describes the development of the Basic Multiresolution Wavelet System and some of its components, as well as some of the techniques used to design and implement these systems.
Abstract
1. Introduction to Wavelets. 2. A Multiresolution Formulation of Wavelet Systems. 3. Filter Banks and the Discrete Wavelet Transform. 4. Bases, Orthogonal Bases, Biorthogonal Bases, Frames, Tight Frames, and Unconditional Bases. 5. The Scaling Function and Scaling Coefficients, Wavelet and Wavelet Coefficients. 6. Regularity, Moments, and Wavelet System Design. 7. Generalizations of the Basic Multiresolution Wavelet System. 8. Filter Banks and Transmultiplexers. 9. Calculation of the Discrete Wavelet Transform. 10. Wavelet-Based Signal Processing and Applications. 11. Summary Overview. 12. References. Bibliography. Appendix A. Derivations for Chapter 5 on Scaling Functions. Appendix B. Derivations for Section on Properties. Appendix C. Matlab Programs. Index.