The Experts below are selected from a list of 126 Experts worldwide ranked by ideXlab platform
Yong-yan Cao - One of the best experts on this subject based on the ideXlab platform.
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Application of Haar wavelet method to eigenvalue problems of high order differential equations
Applied Mathematical Modelling, 2012Co-Authors: Zhi Shi, Yong-yan CaoAbstract:Abstract In this work, we present a computational method for solving eigenvalue problems of high-order ordinary differential equations which based on the use of Haar wavelets. The variable and their derivatives in the governing equations are represented by Haar Function and their integral. The first transform the spectral coefficients into the nodal variable values. The second, solve the obtained system of algebraic equation. The efficiency of the method is demonstrated by four numerical examples.
Joon-hoon Park - One of the best experts on this subject based on the ideXlab platform.
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Application of Two Dimensional Haar Transforms and Fast Haar Functions to Analysis High OrderSystemin Time and Frequency Domain
International Journal of Control and Automation, 2014Co-Authors: Joon-hoon ParkAbstract:In this paper, a method for analysis high order transfer Function system via two dimensional Haar transforms is proposed. A high order transfer Function system can be transformed and simplified to a low order system that has same system response. For these, fast Haar Function seriesthat is a complete set of orthogonal rectangular Functions similar in several respects of the Walsh Functionsand two dimensional Haar transform algorithm are applied. And the results are simulated in time and frequency domain. The suggested method is more efficient and convenient for simplification of high order system.
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Transfer Function Approximation Via Rationalized Haar Transform in Frequency Domain
International Journal of Control and Automation, 2014Co-Authors: Joon-hoon ParkAbstract:For system analysis and design purposes, it is meaningful discussion to define control system pole status whether a pole is significant or not. If a pole is less important, it can be canceled from the transfer Function of system and system order is reduced. In this paper a method for system order reduction of transfer Function using Rationalized Haar Functions based on approximation and transform algorithm is presented. The Haar Function set forms a complete set of orthogonal rectangular Functions such as Walsh and block pulse Functions. But the Haar Functions have some disadvantages of calculation because of including irrational numbers such as The Rationalized Haar Functions were introduced by M. Ohkita to overcome these disadvantages. The Rationalized Haar Functions constitute of rational numbers only. The applied method to solve the system order reduction of transfer Function problem is superior to conventional numerical methods.
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Approximation of High Order Characteristic Equation using Discrete Haar Transforms
2014Co-Authors: Joon-hoon ParkAbstract:An algorithm for approximation high order characteristic equation by low order characteristic Function using discrete Haar transform is presented in this paper. The characteristic equation often contains less significant poles that have little effect on the system response. Haar Function set forms a complete set of orthogonal rectangular Functions similar in several respects of the Walsh Functions. The method adopted in this paper is that of system approximation using discrete Haar transform. This approach provides a more efficient and convenient method for the system order reduction.
Zhi Shi - One of the best experts on this subject based on the ideXlab platform.
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Application of Haar wavelet method to eigenvalue problems of high order differential equations
Applied Mathematical Modelling, 2012Co-Authors: Zhi Shi, Yong-yan CaoAbstract:Abstract In this work, we present a computational method for solving eigenvalue problems of high-order ordinary differential equations which based on the use of Haar wavelets. The variable and their derivatives in the governing equations are represented by Haar Function and their integral. The first transform the spectral coefficients into the nodal variable values. The second, solve the obtained system of algebraic equation. The efficiency of the method is demonstrated by four numerical examples.
Baochang Shi - One of the best experts on this subject based on the ideXlab platform.
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Fast algorithm of (k, k-1) type discrete Walsh-Haar transformation and application in image edge detection
MIPPR 2011: Remote Sensing Image Processing Geographic Information Systems and Other Applications, 2011Co-Authors: Baochang ShiAbstract:Walsh-Haar Function system that was first introduced by us is a new kind of Function systems, and has a good global / local property. This Function system is called Walsh ordering Function system since its generation kernel Functions belong to Walsh ordering Walsh Function system. We worked out a recursive property of the matrix WH KR m+1 WH corresponding to the first KR m+1 Walsh-Haar Functions in Walsh-Haar Function system, and proved that Walsh-Haar Function system is perfect and orthogonal similar to Walsh Function system and Haar Function system. Thus, discrete Walsh-Haar transformation (DW-HT) is an orthogonal transformation that can be widely used in signal processing. In this paper, using the recursive property of the matrix WH KRm+1 WH and the fast algorithm of discrete Walsh transformation in Walsh ordering, we have designed a fast algorithm of Walsh ordering (k, k-1) type DW-HT based on the bisection technique. As one of its applications, we use it to detect image edges. Compare with some edge-detecting methods, the method in this paper detects more details of image edge. The idea and method used to design the fast algorithm in this paper can be used to design fast algorithms of other ordering (k, k-1) type DW-HTs and other discrete orthogonal transformations.
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Fast algorithm of discrete Walsh-Haar transformation
International Conference on Space Information Technology, 2005Co-Authors: Baochang Shi, Jinwen Tian, Jian LiuAbstract:Walsh-Haar Function system that was first intruoduced by us is a new kind of Function systems, and has a good global/local property. This Function system is called Walsh ordering Function system since its generation kernel Functions belong to Walsh ordering Walsh Function system. We worked out a recursive property of the matrix corresponding to the first Walsh-Haar Functions in Walsh-Haar Function system, and we also proved that Walsh-Haar Function system is perfect and orthogonal similar to Walsh Function system and Haar Function system. Thus, discrete Walsh-Haar transformation (DW-HT) is an orthogonal transformation that can be widely used in signal processing. In this paper, using the recursive property of the matrix and the fast algorithm of discrete Walsh transformation (DWT) in Walsh ordering, we have designed a fast algorithm of Walsh ordering DW-HT based on the bisection technique. The idea and method used in this paper can be used for designing fast algorithms of other ordering DW-HTs and other discrete orthogonal transformations.
Karl Entacher - One of the best experts on this subject based on the ideXlab platform.
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Discrepancy estimates based on Haar Functions
Mathematics and Computers in Simulation, 2001Co-Authors: Karl EntacherAbstract:We present a technique to estimate the star-discrepancy of (t, m, s)-nets using generalized Haar Function systems and apply this technique to obtain upper bounds for the star-discrepancy of special digital ( t, m, s)-nets in base 2 and dimension s D 2. © 2001 IMACS. Published by Elsevier Science B.V. All rights reserved.
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Haar Function Based Estimates of the Star-Discrepancy of Plane Digital Nets
Monatshefte f�r Mathematik, 2000Co-Authors: Karl EntacherAbstract:We apply the Haar Function system to estimate the star-discrepancy of special digital (t,m,s)-nets in dimension \(\). We use a basic technique based on discretization combined with an exact calculation of the discrete star-discrepancy.
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Generalized Haar Function systems, digital nets, and quasi-Monte Carlo integration
Wavelet Applications III, 1996Co-Authors: Karl EntacherAbstract:Quasi-Monte Carlo methods are an extremely effective approach for computing high dimensional integrals. In this paper we present a concept based on generalized Haar Functions systems that allow us to estimate the integration error for practically relevant classes of Functions. The local structure of the Haar Functions yields interesting new aspects in proofs and results. The results are supplemented by concrete computer calculations.© (1996) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
