A Haar wavelet operational matrix is applied to fractional integration, which has not been undertaken before. The Haar wavelet approximating method is used to reduce the fractional Volterra and Abel integral equations to a system of algebraic equations. A global error bound is estimated and some numerical examples with smooth, nonsmooth, and singular solutions are considered to demonstrate the ...

In order to extract the intrinsic information of climatic time series from background red noise, we will first give an analytic formula on the distribution of Haar wavelet power spectra of red noise in a rigorous statistical framework. The relation between scale aand Fourier period T for the Morlet wavelet is a= 0.97T . However, for Haar wavelet, the corresponding formula is a= 0.37T . Since fo...

The aim of this study is to evaluate a machine-learning method in which symbolic representations of folk songs are segmented and classified into tune families with Haar-wavelet filtering. The method is compared with previously proposed Gestaltbased method. Melodies are represented as discrete symbolic pitch-time signals. We apply the continuous wavelet transform (CWT) with the Haar wavelet at s...

We present here, a Haar wavelet method for a class of third order partial dierentialequations (PDEs) arising in impulsive motion of a flat plate. We also, present Adomaindecomposition method to find the analytic solution of such equations. Efficiency andaccuracy have been illustrated by solving numerical examples.

A method for seamless stitching of images with photometric inconsistencies in the overlapping region is presented. The method is based on generating a set of stitched gradients from the gradients of the input images and then reconstructing the mosaic image using the Haar wavelet integration technique of [11], [12]. This O(N) reconstruction technique is based on obtaining the Haar wavelet decomp...

In this paper, after reviewing the main points of Haar wavelet transform and chaotic trigonometric maps, we introduce a new perspective of Haar wavelet transform. The essential idea of the paper is given linearity properties of the scaling function of the Haar wavelet. With regard to applications of Haar wavelet transform in image processing, we introduce chaotic trigonometric Haar wavelet tran...

in this article,we present a wavelet method for solving stochastic volterra integral equations based on haar wavelets. first, we approximate all functions involved in the problem by haar wavelets then, by substituting the obtained approximations in the problem, using the it^{o} integral formula and collocation points then, the main problem changes into a system of linear or nonlinear equation w...

I present a method for producing estimates of the intensity function of certain `burst-like' inhomogeneous Poisson processes, based on the shrinkage of Haar wavelet coe cients of the observed counts. The Haar basis is a natural wavelet basis in which to work in this context, and I derive thresholds for shrinkage estimation based on the distribution of the coe cients. The translation-invariant d...