A non-linear transform, called ‘Sign Hadamard-Haar transform’ is introduced. The transform is unique and converts ternary vectors into ternary spectral domain. Recursive definition and fast transform have been developed. Formulae to represent Sign Hadamard-Haar spectra for basic logic functions and their variables for two different codings are shown. New transform is extremely effective in term...

It is shown that the span of fa i h i b i e i g n i=1 , where fh i g is the Haar system in L p and fe i g the canonical basis of`p , is well isomorphic to a well complemented subspace of L p ; 2 < p < 1. As a consequence we get that there is a rearrangement of the (initial segments of the) Haar system in L p ; 2 < p < 1, any block basis of which is well isomorphic to a well complemented subspac...

in this work, we present a computational method for solving second kindnonlinear fredholm volterra integral equations which is based on the use ofhaar wavelets. these functions together with the collocation method are thenutilized to reduce the fredholm volterra integral equations to the solution ofalgebraic equations. finally, we also give some numerical examples that showsvalidity and applica...

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 ...

Haar transform is known to have the smallest computational requirement and has been used mainly for pattern recognition and image processing. Although the properties of Haar spectra of Boolean functions have considerable interest and attraction, the majority of publications to date have employed the Walsh rather than Haar transform in their considerations. It is mainly due to the fact that up t...

We propose a new feature extraction method based on two dynamical systems induced by intensity landscape: the negative gradient system and the Hamiltonian system. We build features based on the Hamiltonian streamlines. These features contain nice global topological information about the intensity landscape, and can be used for object detection. We show that for training images of same size, our...

A Haar wavelet based numerical method for solving singularly perturbed linear time invariant system is presented in this paper. The reduced pure slow and pure fast subsystems are obtained by decoupling the singularly perturbed system and differential matrix equations are converted into algebraic Sylvester matrix equations via Haar wavelet technique. The operational matrix of integration and its...

Methods based on hypothesis tests (HTs) in the Haar domain are widely used to denoise Poisson count data. Facing large datasets or real-time applications, Haar-based denoisers have to use the decimated transform to meet limited-memory or computation-time constraints. Unfortunately, for regular underlying intensities, decimation yields discontinuous estimates and strong "staircase" artifacts. In...

Abstract: In this paper, identification of a continuous-time linear time-varying (LTV) system is proposed, where Haar wavelet with unit energy is employed. For that purpose, an algebraic equation is derived by expanding the input-output data and the time-varying impulse response using normalized Haar wavelets. Unknown wavelet coefficients for the a LTV system’s impulse response can be effective...

abstract. in this paper, we implement numerical solution of differential equations of frac- tional order based on hybrid functions consisting of block-pulse function and rationalized haar functions. for this purpose, the properties of hybrid of rationalized haar functions are presented. in addition, the operational matrix of the fractional integration is obtained and is utilized to convert compu...