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Ten Lectures on Wavelets

Ingrid Daubechies, Christopher Heil

Abstract

Introduction Preliminaries and notation The what, why, and how of wavelets The continuous wavelet transform Discrete wavelet transforms: Frames Time-frequency density and orthonormal bases Orthonormal bases of wavelets and multiresolutional analysis Orthonormal bases of compactly supported wavelets More about the regularity of compactly supported wavelets Symmetry for compactly supported wavelet bases Characterization of functional spaces by means of wavelets Generalizations and tricks for orthonormal wavelet bases References Indexes.

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Key concepts: Wavelet, Legendre wavelet, Orthonormal basis, Mathematics, Discrete wavelet transform, Gabor wavelet, Fast wavelet transform, Pure mathematics