Related papers: A note on reassignment for wavelets
An element of a group is said to be reversible if it is conjugate to its inverse. We characterise the reversible elements in the group of diffeomorphisms of the real line, and in the subgroup of order preserving diffeomorphisms.
The work addresses the definition of a wavelet that is adapted to analyse a flexural impulse response. The wavelet gives the opportunity to directly analyse the dispersion characteristics of a pulse. The aim is to localize a source or to…
Recently, it has been proven [R. Soc. Open Sci. 1 (2014) 140124] that the continuous wavelet transform with non-admissible kernels (approximate wavelets) allows for an existence of the exact inverse transform. Here we consider the…
Wavelet and frames have become a widely used tool in mathematics, physics, and applied science during the last decade. This article gives an overview over some well known results about the continuous and discrete wavelet transforms and…
A wavelet is a localized function having a prescribed number of vanishing moments. In this correspondence, we provide precise arguments as to why the Hilbert transform of a wavelet is again a wavelet. In particular, we provide sharp…
We show that continuous transform with the complex Morlet wavelet is easily performed if we replace the integration of the fast-oscillation function by the solution of the diffusion differential equations. The most important advantage of…
Adaptive mesh refinement techniques are nowadays an established and powerful tool for the numerical discretization of PDE's. In recent years, wavelet bases have been proposed as an alternative to these techniques. The main motivation for…
In the present paper, details are given on the implementation of a wavelet-based analysis tailored to the processing of acoustical signals. The family of the suitable wavelets (`Reimann wavelets') are obtained in the time domain from a…
We shall study the equivalence problem for ordinary differential equations with respect to the affine transformations group.
The problem considered here is the determination of the hamiltonian of a first quantized nonrelativistic particle by the help of some measurements of the location with a finite resolution. The resulting hamiltonian depends on the resolution…
We prove that the unitary affine Radon transform intertwines the quasi-regular representation of a class of semidirect products, built by shearlet dilation groups and translations, and the tensor product of a standard wavelet representation…
In this short note we discuss the interplay between finite Coxeter groups and construction of wavelet sets, generalized multiresolution analysis and sampling.
An element $g$ in a group $G$ is called reversible if $g$ is conjugate to $g^{-1}$ in $ G $. An element $g$ in $G$ is strongly reversible if $ g $ is conjugate to $g^{-1}$ by an involution in $G$. The group of affine transformations of…
In the classical theorems of extreme value theory the limits of suitably rescaled maxima of sequences of independent, identically distributed random variables are studied. So far, only affine rescalings have been considered. We show,…
New elliptic cylindrical wavelets are introduced, which exploit the relationship between analysing filters and Floquet's solution of Mathieu differential equations. It is shown that the transfer function of both multiresolution filters is…
An overview is given on recent developments in the affine Weyl group approach to Painlev\'e equations and discrete Painlev\'e equations, based on the joint work with Y. Yamada and K. Kajiwara.
The wavelet transform, a family of orthonormal bases, is introduced as a technique for performing multiresolution analysis in statistical mechanics. The wavelet transform is a hierarchical technique designed to separate data sets into sets…
We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…
In this paper we introduce an enhanced notion of extremal systems for sets in locally convex topological vector spaces and obtain efficient conditions for set extremality in the convex case. Then we apply this machinery to deriving new…
Several differentiating algorithms of the noisy signals are considered. The proposed wavelet based technique is compared with others based on the Fourier transform and the finite differences. The accuracy of the calculations for different…