Related papers: Wavelets for Elliptical Waveguide Problems
Bayesian approaches are one of the primary methodologies to tackle an inverse problem in high dimensions. Such an inverse problem arises in hydrology to infer the permeability field given flow data in a porous media. It is common practice…
A new method is presented for the construction of a natural continuous wavelet transform on the sphere. It incorporates the analysis and synthesis with the same wavelet and the definition of translations and dilations on the sphere through…
Solving the wave equation is one of the most (if not the most) fundamental problems we face as we try to illuminate the Earth using recorded seismic data. The Helmholtz equation provides wavefield solutions that are dimensionally reduced,…
We study the polarization properties of elliptical femtosecond-laser-written waveguides arrays. A new analytical model is presented to explain the asymmetry of the spatial transverse profiles of linearly polarized modes in these waveguides.…
Wavelet analysis and compression tools are reviewed and different applications to study MHD and plasma turbulence are presented. We introduce the continuous and the orthogonal wavelet transform and detail several statistical diagnostics…
We propose a method of solving partial differential equations on the $n$-dimen\-sional unit sphere with methods based on the continuous wavelet transform derived from approximate identities.
A set of semi-analytical techniques based on Fourier analysis is used to solve wave scattering problems in variously shaped waveguides with varying normal admittance boundary conditions. Key components are newly developed conformal mapping…
We present a new proof of a theorem of Mallat which describes a construction of wavelets starting from a quadrature mirror filter. Our main innovation is to show how the scaling function associated to the filter can be used to identify a…
Wavelets are known to be closely related to atomic orbital. A new approach of 2D, 3D and multidimensional wavelet system is proposed from a paralell with anti-symmetric systems of several isolated particles. The theory of fermionic states…
We develop a general notion of orthogonal wavelets `centered' on an irregular knot sequence. We present two families of orthogonal wavelets that are continuous and piecewise polynomial. We develop efficient algorithms to implement these…
We introduce an equivalence relation on the set of single wavelets of L^2(R^n) associated with an arbitrary dilation matrix. The corresponding equivalence classes are characterized in terms of the support of the Fourier transform of…
Two methods are explained to exactly solve Maxwell's equations where permittivity, permeability and conductivity may vary in space. In the constitutive relations, retardation is regarded. If the material properties depend but on one…
This paper offers a new regard on compactly supported wavelets derived from FIR filters. Although being continuous wavelets, analytical formulation are lacking for such wavelets. Close approximations for daublets (Daubechies wavelets) and…
Matched wavelets interpolating equidistant data are designed. These wavelets form Riesz bases. Meyer wavelets that interpolate data on a particular uniform lattice are found.
Nonlinear filtering is a pivotal problem that has attracted significant attention from mathematicians, statisticians, engineers, and various other scientific disciplines. The solution to this problem is governed by the so-called filtering…
The Mathieu functions are used to solve analytically some problems in elliptical cylinder coordinates. A computational toolbox was implemented in Matlab. Since the notation and normalization for Mathieu functions vary in the literature, we…
This paper presents novel designs, analysis, and performance of 4-pole and 8-pole microwave and millimeter-wave (MMW) waveguide filters for operation at X and Y frequency bands. The waveguide filters have been designed and analyzed based on…
We consider two phaseless inverse problems for elliptic equation. The statements of these problems differ from have considered. Namely, instead of given information about modulus of scattering waves, we consider the information related to…
The multiresolution analysis of Alpert is considered. Explicit formulas for the entries in the matrix coefficients of the refinement equation are given in terms of hypergeometric functions. These entries are shown to solve generalized…
The spectral properties of the Ruelle transfer operator which arises from a given polynomial wavelet filter are related to the convergence question for the cascade algorithm for approximation of the corresponding wavelet scaling function.