• Proceedings of the KIEE Conference
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• 2002.07d
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• pp.2129-2131
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• 2002

This paper proposes a real-time application of rationalized Haar transform which is based on the rationalized Haar transform, operational matrix and rationalized Haar function's differential operation. In the existing method of orthogonal functions, a major disadvantage is that process signals need to be recorded prior to obtaining their expansions. This paper proposes a novel method of rationalized Haar transform to overcome this shortcoming. And the proposed method apply to the robust MRAC systems.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.51 no.6
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• pp.228-234
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• 2002

This paper proposes a real-time application of rationalized Haar transform which is based on the local rationalized Haar transform, local operational matrix and local delay operational matrix. This approach let a general sampling time be used by introducing a scaling factor. In the existing method of orthogonal functions, a major disadvantage is that process signals need to be recorded prior to obtaining their expansions. This paper proposes a novel method of rationalized Haar transform to overcome this shortcoming. And the proposed method is suitable for the analysis of linear systems. The proposed method is expected to the applicable to the adaptive control which demanded to the real-time applications.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.145-159
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• 2011

The numerical solution to the linear and nonlinear and linear system of Fredholm and Volterra integral equations of the second kind are investigated. We have used crooked lines which includ the nodes specified by modified rationalized Haar functions. This method differs from using nominal Haar or Walsh wavelets. The accuracy of the solution is improved and the simplicity of the method of using nominal Haar functions is preserved. In this paper, the crooked lines with unknown coefficients under the specified conditions change the system of integral equations to a system of equations. By solving this system the unknowns are obtained and the crooked lines are determined. Finally, error analysis of the procedure are considered and this procedure is applied to the numerical examples, which illustrate the accuracy and simplicity of this method in comparison with the methods proposed by these authors.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1055-1071
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• 2010

Recently, a number of algorithms have been proposed for numerical evaluation of Hankel transforms as these transforms arise naturally in many areas of science and technology. All these algorithms depend on separating the integrand $rf(r)J_{\upsilon}(pr)$ into two components; the slowly varying component rf(r) and the rapidly oscillating component $J_{\upsilon}(pr)$. Then the slowly varying component rf(r) is expanded either into a Fourier Bessel series or various wavelet series using different orthonormal bases like Haar wavelets, rationalized Haar wavelets, linear Legendre multiwavelets, Legendre wavelets and truncating the series at an optimal level; or approximating rf(r) by a quadratic over the subinterval using the Filon quadrature philosophy. The purpose of this communication is to take a different approach and replace rapidly oscillating component $J_{\upsilon}(pr)$ in the integrand by its Bernstein series approximation, thus avoiding the complexity of evaluating integrals involving Bessel functions. This leads to a very simple efficient and stable algorithm for numerical evaluation of Hankel transform.