Ten Lectures on Wavelets

  title={Ten Lectures on Wavelets},
  author={Ingrid Daubechies},
  journal={Computers in Physics},
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 bases of compactly supported wavelets II: variations on a theme
Several variations are given on the construction of orthonormal bases of wavelets with compact support. They have, respectively, more symmetry, more regularity, or more vanishing moments for the
Convergence: Fourier series vs. wavelet expansions
Wavelet bases were introduced in the 1980’s as new orthonormal bases of various spaces. Much has been studied on the theory of wavelets, and many applications have been made. Several interesting
A brief description of wavelet and wavelet transforms and their applications
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Orthonormal polynomial wavelets on the interval
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Rapidly Decaying Harmonic Wavelet Expansion
Among orthogonal wavelets, Shannon’s wavelets are very simple but have the demerit that they are not well localized and decay slowly. Meyer’s wavelets, which are obtained by modifying Shannon’s
Construction of orthonormal wavelet-like bases
A general method for constructing wavelet-like bases in a Hilbert space H starting from any orthonormal basis in H and any periodic orthonormal wavelet basis is presented. With this method we can
Construction of vector valued wavelet packets on ℝ+ using Walsh-Fourier transform
In this paper, the concept of vector-valued wavelet packets in space L2(ℝ+, ℂN) is introduced. Some properties of vector-valued wavelets packets are studied and orthogonality formulas of these
Approximate moments and regularity of efficiently implemented orthogonal wavelet transforms
An efficient implementation of orthogonal wavelet transforms is obtained by approximating the rotation angles of the orthonormal rotations used in a lattice implementation of the filters by exploiting their finite scale regularity, i.e. "smoothness" only up to a certain finite scale.
Wavelet transforms for discrete-time periodic signals