• Journal of the Institute of Electronics Engineers of Korea SP
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• v.45 no.4
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• pp.78-83
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• 2008

Interpolation filters are widely used in symbol timing recovery systems to interpolate new sample values at arbitrary points between the existing discrete-time samples. Polynomial interpolation is interpolated by coefficient made inputted information. This paper presents an efficient way to implement polynomial base interpolation filters using support filter changing input. By an example, it is shown that the proposed structure out performs the conventional interpolation structure with less hardware cost.

• Proceedings of the KIEE Conference
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• 2003.07e
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• pp.55-57
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• 2003

This paper presents a new method for finding the Block Pulse series coefficients and deriving the Block Pulse integration operational matrices which are necessary for the control fields using the Block Pulse functions. In this paper, the accuracy of the Block Pulse series coefficients derived by using the Lagrange second order interpolation polynomial is approved by the mathematical method.

• Transactions of the Korean Society of Automotive Engineers
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• v.6 no.5
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• pp.128-137
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• 1998

A numerical approach for performing kinematic design sensitivity analysis of vehicle suspension systems is presented. Compared with the conventional analytical methods, which require explicit derivation of sensitivity equations, the proposed numerical method can be applied to any type of suspension systems without obtaining sensitivity equations, once any kinematic analysis procedure is established. To obtain sensitivity equations, a numerical differentiation algorithm that uses the third order Lagrange polynomial is developed. The algorithm efficiently and accurately computes the sensitivity of various vehicle static design factors with respect to kinematic design variables. Through a suspension design problem, the validity and usefulness of the method is demonstrated.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.4
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• pp.709-714
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• 2017

The curved panel is widely used for display of TVs and smart phones. This paper proposes a new auto-focusing method for curved panel inspection system. Since the distance between the camera and the panel varies with the curve position, the camera should change its focus at every inspection time. In order to reduce the focusing time, we propose an effective focusing method that considers the mathematical model of panel curve. The Lagrange polynomial equation is applied to modeling the panel curve. The foci of initial three points are used to get the curve equation, and the other foci are calculated automatically from the curve equation. The experiment result shows that the proposed method can reduce the focusing time.

• The Transactions of the Korea Information Processing Society
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• v.13 no.2
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• pp.34-40
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• 2024

Secret sharing is a cryptographic technique that involves dividing a secret or a piece of sensitive information into multiple shares or parts, which can significantly increase the confidentiality of a secret. There has been a lot of research on secret sharing for different contexts or situations. Tassa's conjunctive secret sharing method employs polynomial derivatives to facilitate hierarchical secret sharing. However, the use of derivatives introduces several limitations in hierarchical secret sharing. Firstly, only a single group of participants can be created at each level due to the shares being generated from a sole derivative. Secondly, the method can only reconstruct a secret through conjunction, thereby restricting the specification of arbitrary secret reconstruction conditions. Thirdly, Birkhoff interpolation is required, adding complexity compared to the more accessible Lagrange interpolation used in polynomial-based secret sharing. This paper introduces the multi-compartment secret sharing method as a generalization of the conjunctive hierarchical secret sharing. Our proposed method first encrypts a secret using external groups' shares and then generates internal shares for each group by embedding the encrypted secret value in a polynomial. While the polynomial can be reconstructed with the internal shares, the polynomial just provides the encrypted secret, requiring external shares for decryption. This approach enables the creation of multiple participant groups at a single level. It supports the implementation of arbitrary secret reconstruction conditions, as well as conjunction. Furthermore, the use of polynomials allows the application of Lagrange interpolation.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.2
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• pp.544-556
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• 1991

The optimization of many engineering design problems requires a nonlinear programming algorithm that is robust and efficient. A general-purpose nonlinear optimization program IDOL (Interactive Design Optimization Library) is developed based on the Augmented Lagrange Mulitiplier (ALM) method. The ideas of selecting a good initial design point, using resonable initial values for Lagrange multipliers, constraints scaling, descent vector restarting, and dynamic stopping criterion are employed for computational enhancement to the ALM method. A descent vector is determined by using the Broydon-Fletcher-Goldfarb-Shanno (BFGS) method. For line search, the Incremental-Search method is first used to find bounds on the solution, then the bounds are reduced by the Golden Section method, and finally a cubic polynomial approximation technique is applied to locate the next design point. Seven typical test problems are solved to show IDOL efficient and robust.

• Journal of the Korea Institute of Military Science and Technology
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• v.21 no.3
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• pp.264-278
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• 2018

The support structure of an optical mirror system is the one of the important design elements because the one affects the optical aberrations of the mirror surface. In this paper, Lagrange equation of the moving body of the fast steering mirror system(FSM) has been formulated to use with optimization design. Major goals for optimization are to assign the reasonably flexible stiffness to the structure and to enhance the first natural frequency of the mirror and support system in aid of more affordable control bandwidth for the FSM. Pursuing these purposes with the proposed method, the finite element analysis(FEA), optimization technique and the Zernike polynomial estimation are used for the design effects. It is concluded that the proposed approach for design well guides toward the desired design goals with regards to both structural and optical performances.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.22 no.4
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• pp.37-41
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• 2021

This paper presents a study to implement a touch screen capable of real-time response processing in a low-end embedded system. This was done by introducing an algorithm using an interpolation method to represent real-time response characteristics when a touch input is performed. In this experiment, we applied a linear interpolation algorithm that estimates random data by deriving a first-order polynomial from 2-point data. We also applied a Lagrange interpolation algorithm that estimates random data by deriving a quadratic polynomial from 3-point data. As a result of the experiment, it was found that the Lagrange interpolation method was more complicated than the linear interpolation method, and the processing speed was slow, so the text was not smooth. When using the linear interpolation method, it was confirmed that the speed displayed on a screen is 2.4 times faster than when using the Lagrange interpolation method. For real-time response characteristics, it was confirmed that smaller size of the executable file of the algorithm is more advantageous than the superiority of the algorithm itself. In conclusion, in order to secure real-time response characteristics in a low-end embedded system, it was confirmed that a relatively simple linear interpolation algorithm performs touch operations with better real-time response characteristics than the Lagrange interpolation method.

• The KIPS Transactions:PartD
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• v.10D no.7
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• pp.1145-1148
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• 2003

We show the mixed finite element method which induces solutions that has the same order of errors for both the gradient of the solution and the solution itself. The technique to construct an efficient reusable matrix is suggested. Two families of mixed finite element methods are introduced with an automatic generating technique for matrix with my order of basis. The generated matrix by this technique has more accurate values and is a sparse matrix. This new technique is applied to solve a minimal surface problem.

• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.10
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• pp.188-198
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• 2013

Maximally flat (MAXFLAT) half-band filters usually have wider transition band than other filters. This is due to the fact that the maximum possible number of zeros at $z={\pm}1$ is imposed, which leaves no degree of freedom, and thus no independent parameters for direct control of the frequency response. This paper describes a novel method for the design of FIR halfband filters with an explicit control of the transition-band width. The proposed method is based on a generalized Lagrange halfband polynomial (g-LHBP) with coefficients parametizing a 0-th coefficient $h_0$, and allows the frequency response of this filter type to be controllable by adjusting $h_0$. Then, $h_0$ is modeled as a steepness parameter of the transition band and this is accomplished through theoretically analyzing a polynomial recurrence relation of the g-LHBP. This method also provides explicit formulas for direct computation of design parameters related to choosing a desired filter characteristic (by trade-off between the transition-band sharpness and passband & stopband flatness). The examples are shown to provide a complete and accurate solution for the design of such filters with relatively sharper transition-band steepness than MAXFLAT half-band filters.