In this work, a sort of binary wavelet packages with multi-scale are introduced, which are generalizations of multivariant wavelet packages. Finitely Supported wavelet bases for Sobolev spaces is researched. Steming from a pair of finitely supported refinale functions with multi-scaled dilation factor in space 2 2 ( ) L R satsfying a very mild condition, we provide a novel method for designing ...

Orthogonal compact-support Daubechies wavelets are employed as bases for both space and time variables in the solution of the time-dependent Schrodinger equation. Initial value conditions are enforced using special early-time wavelets analogous to edge wavelets used in boundary-value problems. It is shown that the quantum equations may be solved directly and accurately in the discrete wavelet r...

In this paper, a method for parameterizing orthogonal wavelet transforms is presented. The parameter space is given by the rotation angles of the orthogonal 2 2 rotations used in the lattice filters realizing the stages of the wavelet transform. Different properties of orthogonal wavelet transforms can be expressed in this parameter space. Then, the parameter space is restricted to the set of r...

The purpose of this presentation is to describe a recent family of basis functions—the fractional B-splines—which appear to be intimately connected to fractional calculus. Among other properties, we show that they are the convolution kernels that link the discrete (finite differences) and continuous (derivatives) fractional differentiation operators. We also provide simple closed forms for the ...

On the n-dimensional hypercube, for given k ∈ N, wavelet Riesz bases are constructed for the subspace of divergence-free vector fields of the Sobolev space Hk((0, 1)n)n with general homogeneous Dirichlet boundary conditions, including slip or no-slip boundary conditions. Both primal and suitable dual wavelets can be constructed to be locally supported. The construction of the isotropic wavelet ...

The WSO M (Wavelet SelfOrganizing 1\Jap) model, a rwural network for the erea.tion of wavelet bases adapted to the distribution of input data, is introduced. The model provides an efficient on-lim) way to construct high-dimensional wavelet bases. Simulations of a lD function approximation problem illustrate how WSOM adapts to non-uniformly distributed input data, outperforming the discrete wa.v...

We present a new family of 2D orthogonal wavelets which uses quincunx sampling. The orthogonal refinement filters have a simple analytical expression in the Fourier domain as a function of the order α, which may be non-integer. The wavelets have good isotropy properties. We can also prove that they yield wavelet bases of L2(R) for any α > 0. The wavelets are fractional in the sense that the app...

On the n-dimensional hypercube, for given k ∈ N, biorthogonal wavelet Riesz bases are constructed for the subspace of divergence-free vector fields of the Sobolev space Hk((0, 1)n)n with general homogeneous Dirichlet boundary conditions, including slip or no-slip boundary conditions. Both primal and dual wavelets can be constructed to be locally supported. The construction of the isotropic wave...