• School Mathematics
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• v.16 no.2
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• pp.317-334
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• 2014

The purpose of this study is to grasp pre-service secondary teachers' understanding-realities for Taylor series convergence conceptions and to examine a teaching way using GeoGebra based on the understanding-realities. In this study, most pre-service teachers have abilities to calculate the Taylor series and radius of convergence, but they are vulnerable to conceptual problems which give meaning of the equality between a given function and its Taylor series at any point. Also they have some weakness in determining the change of radius of convergence according to the change of Taylor series' center. To improve their weakness, we explore a teaching way using dynamic and CAS functionality of GeoGebra. This study is expected to improve the pedagogical content knowledge of pre-service secondary mathematics teachers for infinite series treated in high school mathematics.

• Communications of Mathematical Education
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• v.31 no.1
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• pp.71-84
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• 2017

Taylor series has a complicated structure comprising of various concepts in college major mathematics. This subject is a strong tool which has usefulness and applications not only in calculus, analysis, and complex analysis but also in physics, engineering etc., and other study. However, students have difficulties in understanding mathematical structure of Taylor series convergence correctly. In this study, after classifying students' mathematical characteristic into three categories, we use structural image of Taylor series convergence which associated with mathematical structure and operation acted on that structure. Thus, we try to analyze the understanding of Taylor series convergence and present the results of this study.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.47 no.9
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• pp.1-8
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• 2010

A digital phase wrapping modulation (DPM) open-loop polar transmitter can be efficiently applied to a wideband orthogonal frequency division multiplexing (OFDM) communication system by converting in-phase and quadrature signals to envelope and phase signals and then employing the signal mapping process. This mapping process is very similar to quantization in a general communication system, and when taking into account the error that appears during mapping process, one can replace the coordinates rotation digital computer (CORDIC) algorithm in the coordinate conversion part with the Taylor series approximation method. In this paper, we investigate the application of the Taylor series approximation to the cartesian to polar coordinate conversion part of a DPM polar transmitter for wideband OFDM systems. The conventional approach relies on the CORDIC algorithm. To achieve efficient application, we perform computer simulation to measure mean square error (MSE) of the both approaches and find the minimum approximation order for the Taylor series approximation compatible to allowable error of the CORDIC algorithm in terms of hardware design. Furthermore, comparing the processing speeds of the both approaches in the implementation with FPGA reveals that the Taylor series approximation with lower order improves the processing speed in the coordinate conversion part.

• Journal of the Korea Convergence Society
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• v.13 no.1
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• pp.43-50
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• 2022

In this paper, it is shown how the performance of the monopulse algorithm in additive noise is evaluated. In the previous study, the performance analysis of the amplitude-comparison monopulse algorithm was conducted via the first-order and second-order Taylor expansion of four variables. By defining two new random variables from the four variables, it is shown that computational complexity associated with two random variables is much smaller than that associated with four random variables. Performance in terms of mean square error is analyzed from Monte-Carlo simulation. The scheme proposed in this paper is more efficient than that suggested in the previous study in terms of computational complexity. The expressions derived in this study can be utilized in getting analytic expressions of the mean square errors.

• Journal of Convergence for Information Technology
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• v.11 no.12
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• pp.14-21
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• 2021

In this paper, it is shown how the performance of the monopulse algorithm in the presence of an additive noise can be obtained analytically. In the previous study, analytic performance analysis based on the first-order Taylor series and the second-order Taylor series has been conducted. By adopting the third-order Taylor series, it is shown that the analytic performance based on the third-order Taylor series can be made closer to the performance of the original monopulse algorithm than the analytic performance based on the first-order Taylor series and the second-order Taylor series. The analytic MSE based on the third-order Taylor approximation reduces the analytic MSE error based on the second-order Taylor approximation by 89.5%. It also shows faster results in all cases than the Monte Carlo-based MSE. Through this study, it is possible to explicitly analyze the angle estimation ability of monopulse radar in an environment where noise jamming is applied.

• ETRI Journal
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• v.5 no.3
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• pp.26-29
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• 1983

본 연구에서는 2진수를 사용하여 기억용량의 감소와 테일러 급수의 2차항에 의한 정확하고계산속도가 빠른 전력조류계산방법을 나타낸다. 이 방법은 쟈코비안이 상수이며 2차항의 간단한 계산에 의해 계산속도가 빠르고, 행렬의 비영요소의 위치를 2진수로 나타내어 기억용량을 대폭 감소시킨다. 그리고 정확한 전력조류계산에 의해 신뢰성이 높아 R/X가 큰 송전선의 시스템에도 적절한 방법이다.

• The Journal of the Acoustical Society of Korea
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• v.33 no.4
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• pp.232-237
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• 2014

A passive sonar of warship is composed of several directional or omni-directional sensors. In order to model the acoustic signal received into a warship sonar, the wave propagation modeling is usually required from arbitrary noise source to all sensors equipped to the sonar. However, the full calculation for all sensors is time-consuming and the performance of sonar simulator deteriorates. In this study, we suggest an asymptotic method to estimate the sonar signal arrived to sensors adjacent to the reference sensor, where it is assumed that all information of eigenrays is known. This method is developed using Taylor series for the time delay of eigenray and similar to Fraunhofer and Fresnel approximation for sonar aperture. To validate the proposed method, some numerical experiments are performed for the passive sonar. The approximation when the second-order term is kept is vastly superior. In addition, the error criterion for each approximation is provided with a practical example.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.18 no.4
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• pp.97-104
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• 2018

In the conventional direction finding, the antenna is installed at a high position on the ground to detect the position of the target with the environment of the LOS(Line of Sight) as much as the signal receiving environment. However, in order to configure such environment, high cost and installation time were required. In this paper, we use TDOA(Time Difference of Arrival) technique to utilize drones in direction finding, so that four drones can be used for directions finding simulation. Simulations based on drone and TDOA direction finding were constructed using additional signal processing Taylor series and Exact Interactive Algorithm. In the simulation, the receiving power is defined by using the 800MHz path-loss model using the GPS information of the ground direction detection, and the position estimation performance is analyzed when the TDOA technique, the Taylor series, and the Exact Interactive Alogrithm are applied.

• Proceedings of the Korean Statistical Society Conference
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• 2004.11a
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• pp.155-160
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• 2004

불균등 확률 계통추출에서는 모집단 총합에 대한 Horvitz-Thompson 추정량의 대안적 분산 추정량들을 사용하게 된다. 이와 같은 모총합에 관한 분산 추정량들의 설계와 관련한 일반적인 방법은 균등 확률 계통추출에 대한 분산 추정량들에서 시작하고 비율 $y_i,/P_i$에 의한 추정량의 정의에서 $y_i$를 재배치하게 한다. 비선형 조사 통계학에서 추정량들 중의 하나로 테일러 급수 공식을 적용한다. 불균등 확률 계통추출에서의 분산은 8가지 방법으로 추정이 가능하므로 이를 이용한 분산추정량을 구해보고, 비복원 불균등 확률에서의 jackknife방법을 살펴보고자 한다. 또한 이들 분산추정량들에 대한 비교를 몇 가지 방법을 이용하여 알아보도록 한다.

• The Journal of the Korea institute of electronic communication sciences
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• v.8 no.11
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• pp.1681-1690
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• 2013

In this paper, a design of speed and position controller based on the EKF(Extended Kalman Filter) for sensorless control in IPMSM(Interior Permanent Magnet Synchronous Motor) is proposed. The proposed method subdivides the state estimation interval for improving the accuracy of state estimation. and each subdivided interval estimated first order term using Taylor series. The proposed state estimator comparison with the second-order extended Kalman filter reduced calculation amount of a priori estimation. And the simulation results were proved that The accuracy of priori estimation is increased.