In this paper, a minimization of Haar wavelet series for simplification of circuits and Haar based decision diagrams representing discrete multiple-valued functions is proposed. The minimization is performed by permutation of indices of generalized Haar functions. Experimental results show that this method provides reasonable reduction in the number of non-zero coefficients. The Haar series red...

A non-linear transform, called ‘‘sign Haar transform’’ has recently been introduced. The transform is unique and converts binary/ternary vectors into ternary spectral domain. Recursive definitions for the calculation of sign Haar transform are developed. Essential properties of logic functions and variables in the spectral domain of a quantized transform based on Haar functions are presented. S...

Unnormalized Haar spectra and Ordered Binary Decision Diagrams (OBDDs) are two standard representations of Boolean functions used in logic design. In this article, mutual relationships between those two representations have been derived. The method of calculating the Haar spectrum from OBDD has been presented. The decomposition of the Haar spectrum, in terms of the cofactors of Boolean function...

In this paper, An effective and simple numerical method is proposed for solving systems of integral equations using radial basis functions (RBFs). We present an algorithm based on interpolation by radial basis functions including multiquadratics (MQs), using Legendre-Gauss-Lobatto nodes and weights. Also a theorem is proved for convergence of the algorithm. Some numerical examples are presented...

Most of the physical systems exhibit some degree of time-varying behavior. Physical phenomena exhibit time-varying behavior for a number of reasons. Some of the systems are inherently time-varying and can not effectively be modeled using time invariant models. This paper deals with the identification of time-varying systems using Haar basis functions. Basis functions approach involves expanding...

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...

Bent Boolean functions play a very significant role in the design of strong symmetric cryptosystems. In this paper, we present an analysis of Bent functions in the Haar domain. We first present a brief overview of Bent Boolean functions and then derive expressions for the Haar spectrum of Bent functions. The Haar spectral coefficients of Bent functions are given in two ways namely; in terms of ...

Abstract The concept of Rademacher type p (1 ≤ p ≤ 2) plays an important role in the local theory of Banach spaces. In [3] Mascioni considers a weakening of this concept and shows that for a Banach space X weak Rademacher type p implies Rademacher type r for all r < p. As with Rademacher type p and weak Rademacher type p, we introduce the concept of Haar type p and weak Haar type p by replacing...