Related papers: Constructing an orthonormal wavelet from an MRA
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…
Multiplicative cascades are often used to represent the structure of multiscaling variables in many physical systems, specially turbulent flows. In processes of this kind, these variables can be understood as the result of a successive…
We consider wavelets in L^2(R^d) which have generalized multiresolutions. This means that the initial resolution subspace V_0 in L^2(R^d) is not singly generated. As a result, the representation of the integer lattice Z^d restricted to V_0…
The main contribution of this paper is a constructive method for building separable multivariate vector-valued wavelet bases in the general framework of \( L^2(\mathbb{R}^d, \mathbb{R}^m) \) for any \( d, m \geq 1 \). While separable…
In this paper, an algorithm based on polyphase matrix for constructing a pair of orthogonal wavelet frames is suggested, and a general form for all orthogonal tight wavelet frames on local fields of positive characteristic is described.…
Wavelet based algorithms in numerical analysis are similar to other transform methods in that vectors and operators are expanded into a basis and the computations take place in this new system of coordinates. However, due to the recursive…
We present a construction of isotropic boundary adapted wavelets, which are orthogonal and yield a multi-resolution analysis. We analyze direct numerical simulation data of turbulent channel flow computed at a friction Reynolds number of…
Our starting point is the measure $\epsilon_x-\alpha_x\rho_x^{\omega_1}+\beta_x\rho_x^{\omega_2}$, where $\rho_x^{\omega_i}$ is the harmonic measure relative to $x \in \omega_1 \subset \overline{\omega}_1 \subset \omega_2$ and $\omega_i$…
We propose an analytical approach to design flattened wavelength splitters with cascaded Mach-Zehnder interferometers when wavelength dependence of the directional couplers cannot be neglected. We start from a geometrical representation of…
A new method of connecting two wavelet sets with a continuous path of wavelet sets is given. The method is based on a pure set theoretic fact known as the Schroder-Cantor-Bernstein theorem and on a characterization of wavelet sets in terms…
The empirical wavelet transform is a data-driven time-scale representation consisting of an adaptive filter bank. Its robustness to data has made it the subject of intense developments and an increasing number of applications in the last…
Inspired by the key principle behind the EM algorithm, we propose a general methodology for conducting wavelet estimation with irregularly-spaced data by viewing the data as the observed portion of an augmented regularly-spaced data set. We…
The increase of resolution by the use of microspheres is related to the use of evanescent waves, satisfying complex Snell law where the trigonometric functions of the incident and refracted angles are complex trigonometric functions,…
We here use notions from the theory linear shift-invariant dynamical systems to provide an easy-to-compute characterization of all rational wavelet filters. For a given N bigger or equql to 2, the number of inputs, the construction is based…
This paper aims at presenting a new approach to the electro-sensing problem using wavelets. It provides an efficient algorithm for recognizing the shape of a target from micro-electrical impedance measurements. Stability and resolution…
The linear subspaces of a multiresolution analysis (MRA) and the linear subspaces of the wavelet analysis induced by the MRA, together with the set inclusion relation, form a very special lattice of subspaces which herein is called a…
A multiresolution analysis associated with linear canonical transform was defined by Shah and Waseem for which the translation set is a discrete set which is not a group. In this paper, we continue the study based on this nonstandard…
The current state of the art for analytical and computational modelling of deformation in nonlinear electroelastic and magnetoelastic membranes is reviewed. A general framework and a list of methods to model large deformation and associated…
In implementations of the functional data methods, the effect of the initial choice of an orthonormal basis has not gained much attention in the past. Typically, several standard bases such as Fourier, wavelets, splines, etc. are considered…
We present a preconditioning method for the multi-dimensional Helmholtz equation with smoothly varying coefficient. The method is based on a frame of functions, that approximately separates components associated with different singular…