相关论文: The relation of the Allan- and Delta-variance to t…
The Delta-variance analysis is an efficient tool for measuring the structural scaling behaviour of interstellar turbulence in astronomical maps. In paper I we proposed essential improvements to the Delta-variance analysis. In this paper we…
Wavelet Transforms are a widely used technique for decomposing a signal into coefficient vectors that correspond to distinct frequency/scale bands while retaining time localization. This property enables an adaptive analysis of signals at…
In continuous-time wavelet analysis, most wavelet present some kind of symmetry. Based on the Fourier and Hartley transform kernels, a new wavelet multiresolution analysis is proposed. This approach is based on a pair of orthogonal wavelet…
Modeling the structure of molecular clouds depends on good methods to statistically compare simulations with observations in order to constrain the models. Here we characterize a suite of hydrodynamical and magnetohydrodynamical (MHD)…
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…
A new construction of a directional continuous wavelet analysis on the sphere is derived herein. We adopt the harmonic scaling idea for the spherical dilation operator recently proposed by Sanz et al. but extend the analysis to a more…
We introduce a new concept of the so-called {\it composite wavelet transforms}. These transforms are generated by two components, namely, a kernel function and a wavelet function (or a measure). The composite wavelet transforms and the…
The continuous wavelet transform has become a widely used tool in applied science during the last decade. In this article we discuss some generalizations coming from actions of closed subgroups of $\mathrm{GL}(n,\mathbb{R})$ acting on…
The underlying mathematics of the wavelet formalism is a representation of the inhomogeneous Lorentz group or the affine group. Within the framework of wavelets, it is possible to define the ``window'' which allows us to introduce a…
We identify the result of the continuous wavelet transform with the difference of solutions of two hyperbolic partial differential equations, for which wavelet's shift and scale are considered as independent variables on 2D plane. The…
This review paper is intended to give a useful guide for those who want to apply discrete wavelets in their practice. The notion of wavelets and their use in practical computing and various applications are briefly described, but rigorous…
Wavelet analysis is proposed as a new tool for studying the large-scale structure formation of the universe. To reveal its usefulness, the wavelet decomposition of one-dimensional cosmological density fluctuations is performed. In contrast…
In this paper novel classes of 2-D vector-valued spatial domain wavelets are defined, and their properties given. The wavelets are 2-D generalizations of 1-D analytic wavelets, developed from the Generalized Cauchy-Riemann equations and…
We obtain a characterization of all wavelets leading to analytic wavelet transforms (WT). The characterization is obtained as a by-product of the theoretical foundations of a new method for wavelet phase reconstruction from magnitude-only…
We show that translations and dilations of a p-adic wavelet coincides (up to the multiplication by some root of one) with a vector from the known basis of discrete p-adic wavelets. In this sense the continuous p-adic wavelet transform…
The aim of this paper is to establish and study the linear canonical Dunkl wavelet transform. We begin by introducing the generalized translation operator and generalized convolution product for the linear canonical Dunkl transform and we…
Wavelet analysis of different patterns reveals some symmetries and singularities otherwise hidden in the pattern. Its general methods are briefly reviewed. Examples from turbulence, cavitation, Cherenkov gluon emission and quark-gluon jets…
In this paper we outline several points of view on the interplay between discrete and continuous wavelet transforms; stressing both pure and applied aspects of both. We outline some new links between the two transform technologies based on…
In this paper, we exploit the theory of convolution of index Whittaker transform for study of continuous and discrete Index Whittaker wavelet transform and discuss some of its basic properties. Certain boundedness, Plancherel as well as…
Wavelets, known to be useful in non-linear multi-scale processes and in multi-resolution analysis, are shown to have a q-deformed algebraic structure. The translation and dilation operators of the theory associate with any scaling equation…