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...

Haar wavelets have been widely used in Biometrics. One advantage of Haar wavelets is the simplicity and the locality of their decomposition and reconstruction filters. However, Haar wavelets are not satisfactory for some applications due to their non-continuous behaviour. Having a particular level of smoothness is important for many applications. B-spline wavelets are capable of being applied t...

A new method is presented for computation of optimal control for linear systems using Haar wavelets. The method is based on a novel operational matrix derived from integration of Haar wavelets. The optimal control problem is converted to a two-point-boundary-value problem, which is then solved using the Haar wavelet transformation. The proposed method is then extended to the numerical solution ...

As two-dimensional coupled system of nonlinear partial differential equations does not give enough smooth solutions, when approximated by linear, quadratic and cubic polynomials and gives poor convergence or no convergence. In such cases, approximation by zero degree polynomials like Haar wavelets (continuous functions with finite jumps) are most suitable and reliable. Therefore, modified numer...

Generalized Haar wavelets were introduced in connection with the problem of detecting specific periodic components in noisy signals. John Benedetto and I showed that the non–normalized continuous wavelet transform of a periodic function taken with respect to a generalized Haar wavelet is periodic in time as well as in scale, and that generalized Haar wavelets are the only bounded functions with...

It is well known that the Haar and Shannon wavelets in L2(R) are at opposite extremes, in the sense that the Haar wavelet is localized in time but not in frequency, whereas the Shannon wavelet is localized in freqency but not in time. We present a rich setting where the Haar and Shannon wavelets coincide and are localized both in time and in frequency. More generally, if R is replaced by a grou...

Texture is the term used to characterize the surface of a given object or phenomenon and is an important feature used in image processing and pattern recognition. Our aim is to compare various Texture analyzing methods and compare the results based on time complexity and accuracy of classification. The project describes texture classification using Wavelet Transform and Co occurrence Matrix. Co...

The new class of weights called A p weights is introduced. We prove that a characterization and an unconditional basis of the weighted Lp space Lp(Rn,w(x)dx) with w ∈ A p (1 < p < ∞) are given by the Haar wavelets and the Haar scaling function. As an application of these results, we establish a greedy basis by using the Haar wavelets and the Haar scaling function again.

Recently it has been shown that in Image Processing, the usual sum and product of the reals are not the only operations that can be used. Several other operations provided by fuzzy logic perform well in this application. We continue this line of research and we propose the use of a pair consisting of a uninorm and an absorbing norm determined by a continuous, strictly increasing generator inste...

This paper describes and compares application of wavelet basis and Block-Pulse functions (BPFs) for solving fractional integro-differential equation (FIDE) with a weakly singular kernel‎. ‎First‎, ‎a collocation method based on Haar wavelets (HW)‎, ‎Legendre wavelet (LW)‎, ‎Chebyshev wavelets (CHW)‎, ‎second kind Chebyshev wavelets (SKCHW)‎, ‎Cos and Sin wavelets (CASW) and BPFs are presented f...