• Journal of the Korean Institute of Telematics and Electronics
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• v.15 no.5
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• pp.29-33
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• 1978

In this paper, the properties of Galois fields defined over any finite field are analysed to derive Galois switching functions and the arithmetic operation methods over any finite field are showed. The polynomial expansions over finite fields by Lagrange's interpolation method are derived and proved. The results are applied to multivalued single variable logic networks.

• 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.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2017.10a
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• pp.681-683
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• 2017

In the digital information age, image processing is essential for various digital devices such as smart phones, cameras, and TVs. However, degradation occurs in analyzing, recognizing, and processing image data, and salt & pepper noise occurs. Therefore, in this paper, we applied linear interpolation method, newton interpolation method, lagrange interpolation method, and spline interpolation method to the image damaged by salt & pepper noise in order to find more effective interpolation method in salt & pepper noise environment, The methods were compared using the PSNR (peak signal to noise ratio).

• Proceedings of the SAREK Conference
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• 2007.11a
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• pp.29-33
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• 2007

In order to protect the environment from the refrigerant pollution, the $CO_2$ may be regarded as one of the most attractive alternative refrigerants for an automotive air-conditioning system. Control methods for a $CO_2$ system should be different because of $CO_2$'s unique properties as a refrigerant. Especially, the high-side pressure of a $CO_2$ system should be controlled for the effective operation of the system. In this study, the high-side pressure setpoint algorithm was developed by using a neural network and a Lagrange interpolation method. These methods were compared. Simulation results showed that a Lagrange interpolation method was more effective than a neural network in the respect of its easiness of programming and shorter execution time.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.16 no.4
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• pp.2370-2378
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• 2015

This paper proposes an algorithm using Lagrange interpolation method to realize trajectory planning for torque minimization of robot manipulators. For the algorithm, position constraints of robot manipulators should be given and the stability of robot manipulators should be satisfied. In order to avoid Runge's phenomenon, we set up time interpolation points using Chebyshev interpolation points. After that, we found suitable angle which corresponds to the points and then we got trajectories of joint's angle, velocity, acceleration using Lagrange interpolation method. We selected performance index for torque consumption optimization of robot manipulator. The method went through repetitive computation process to have minimum value of the performance index by calculated trajectory. Through the process, we could get optimized trajectory to minimize torque and performance index and guarantee safety of the motion for manipulator performance.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.19 no.2
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• pp.455-462
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• 2015

Image media is used for the internet, computers and digital cameras as part of the core services of multimedia. Digital images can be easily acquired and processed, due to the development of digital home appliances and personal computers' application software. However, image degradation occurs by various external causes in the acquisition, processing and transmitting process of digital images, and its main cause is known to be noise. Therefore, this study proposed and conducted the simulation of image restoration filter algorithm that processes impulse noise and Gaussian noise by applying Lagrange interpolation and spatial weighted method according to distance, respectively. The proposed algorithm improved 8.77[dB], 8.83[dB] and 10.02[dB], respectively, compared to existing A-TMF, AWMF and MMF, as a result of processing by applying the damaged Girl images to impulse noise(P=60%) and Gaussian noise(${\sigma}=10$).

• Proceedings of the Korean Society of Surveying, Geodesy, Photogrammetry, and Cartography Conference
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• 2004.11a
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• pp.129-133
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• 2004

9 GPS data with a 30 second sampling rate were extracted from the GPS raw data that recorded with 1 second interval for interpolation. 9 GPS data were interpolated using lagrange interpolation method and compared to the GPS raw data. Using a 9th-order interpolation, error of interpolated code data were within 0.5m.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.15 no.2
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• pp.1066-1073
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• 2014

This paper presents a new design method of optimal control of system which are changed the system parameters. The method used for this purpose are the Lagrange interpolation method and Pole's Moving range method. We selects a system within the scope of the changing the system parameters. Using pole's moving range we calculated the state weighting matrix of optimal control. The optimal controller is designed by Lagrange interpolation method of the state weighting matrix. We are compared with a traditional optimal controller and proposed method by simulation. The simulation showed that the proposed method is better control performance than traditional method of optimal controller.

• Proceedings of the KIEE Conference
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• 2005.05a
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• pp.161-163
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• 2005

In this paper, we propose an efficient motion vector recovery algorithm for the new coding standard H.264, which makes use of the Lagrange interpolation formula. In H.264/AVC, a 16$\times$16 macroblock can be divided into different block shapes for motion estimation, and each block has its own motion vector. In the natural video the motion vector is likely to move in the same direction, hence the neighboring motion vectors are correlative. Because the motion vector in H.264 covers smaller area than previous coding standards, the correlation between neighboring motion vectors increases. We can use the Lagrange interpolation formula to constitute a polynomial that describes the motion tendency of motion vectors, and use this polynomial to recover the lost motion vector. The simulation result shows that our algorithm can efficiently improve the visual quality of the corrupted video.

• Journal of KSNVE
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• v.5 no.4
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• pp.503-514
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• 1995

In the case of performing experimental modal analysis(EMA) and finite- element analysis(EFA) for a whole structure of automotive body that is composed of many complex parts, a trouble may arise from the calculation time, the capacity of memory in computers and the experimental conditions, etc. In this paper, for the vibrational analysis of automotive body model, the efficient modal synthesis method by means of dividing the whole structure into two parts and performing EMA and FEA for each part is studied. In addition, the method based on Lagrange interpolation is proposed for approximating rotational degrees-of-freedom information and linking FEA with EMA. In result, by measuring translational degrees-of-freedom information of only few points and adopting only few modes, the linking method based on Lagrange interpolation turned out to be efficient and accurate in the low frequency range.