• Title/Summary/Keyword: Fourier coefficients

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Generation of Klobuchar Ionospheric Error Model Coefficients Using Fourier Series and Accuracy Analysis

  • Lee, Chang-Moon;Park, Kwan-Dong
    • Journal of Astronomy and Space Sciences
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    • v.28 no.1
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    • pp.71-77
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    • 2011
  • Ionospheric error modeling is necessary to create reliable global navigation satellite system (GNSS) signals using a GNSS simulator. In this paper we developed algorithms to generate Klobuchar coefficients ${\alpha}_n$, ${\beta}_n$ (n = 1, 2, 3, 4) for a GNSS simulator and verified accuracy of the algorithm. The eight Klobuchar coefficients were extracted from three years of global positioning system broadcast (BRDC) messages provided by International GNSS service from 2006 through 2008 and were fitted with Fourier series. The generated coefficients from our developed algorithms are referred to as Fourier Klobuchar model (FOKM) coefficients, while those coefficients from BRDC massages are named as BRDC coefficients. The correlation coefficient values between FOKM and BRDC were higher than 0.97. We estimated total electron content using the Klobuchar model with FOKM coefficients and compared the result with that from the BRDC model. As a result, the maximum root mean square was 1.6 total electron content unit.

CHANGE-POINT ESTIMATION WITH SAMPLE FOURIER COEFFICIENTS

  • Kim, Jae-Hee
    • Proceedings of the Korean Statistical Society Conference
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    • 2002.11a
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    • pp.109-114
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    • 2002
  • In this paper we propose a change-point estimator with left and right regressions using the sample Fourier coefficients on the orthonormal bases. The asymptotic properties of the proposed change-point estimator are established. The limiting distribution and the consistency of the estimator are derived.

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Partial Sum of Fourier series, the Reinterpret of $L^1$-Convergence Results using Fourier coefficients and theirs Minor Lineage (푸리에 급수의 부분합, 푸리에 계수를 이용한 $L^1$-수렴성 결과들의 재해석과 그 소계보)

  • Lee, Jung-Oh
    • Journal for History of Mathematics
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    • v.23 no.1
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    • pp.53-66
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    • 2010
  • This study concerns with partial sum of Fourier series, Fourier coefficients and the $L^1$-convergence of Fourier series. First, we introduce the $L^1$-convergence results. We consider equivalence relations of the partial sum of Fourier series from the early 20th century until the middle of. Second, we investigate the minor lineage of $L^1$-convergence theorem from W. H. Young to G. A. Fomin. Finally, we compare and reinterpret the $L^1$-convergence theorems.

On $L^1(T^1)$ - Convergence of Fourier Series with BV - Class Coefficients (BV - 족 계수를 갖는 푸리에 급수의 $L^1(T^1)$ - 수렴성에 관하여)

  • Lee, Jung-Oh
    • Journal of the Chosun Natural Science
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    • v.1 no.3
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    • pp.216-220
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    • 2008
  • In general the Banach space $L^1(T^1)$ doesn't admit convergence in norm. Thus the convergence in norm of the partial sums can not be characterized in terms of Fourier coefficients without additional assumptions about the sequence$\{^{\^}f(\xi)\}$. The problem of $L^1(T^1)$-convergence consists of finding the properties of Fourier coefficients such that the necessary and sufficient condition for (1.2) and (1.3). This paper showed that let $\{{\alpha}_{\kappa}\}{\in}BV$ and ${\xi}{\Delta}a_{\xi}=o(1),\;{\xi}{\rightarrow}{\infty}$. Then (1.1) is a Fourier series if and only if $\{{\alpha}_{\kappa}\}{\in}{\Gamma}$.

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Kolmogorov-Smirnov Type Test for Change with Sample Fourier Coefficients

  • Kim, Jae-Hee
    • Journal of the Korean Statistical Society
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    • v.25 no.1
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    • pp.123-131
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    • 1996
  • The problerm of testing for a constant mean is considered. A Kolmogorov-Smirnov type test using the sample Fourier coefficients is suggested and its asymptotic distribution is derived. A simulation study shows that the proposed test is more powerful than the cusum type test when there is more than one change-point or there is a cyclic change.

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Newton's Method to Determine Fourier Coefficients and Wave Properties for Deep Water Waves

  • JangRyong Shin
    • Journal of Ocean Engineering and Technology
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    • v.37 no.2
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    • pp.49-57
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    • 2023
  • Since Chappelear developed a Fourier approximation method, considerable research efforts have been made. On the other hand, Fourier approximations are unsuitable for deep water waves. The purpose of this study is to provide a Fourier approximation suitable even for deep water waves and a numerical method to determine the Fourier coefficients and the wave properties. In addition, the convergence of the solution was tested in terms of its order. This paper presents a velocity potential satisfying the Laplace equation and the bottom boundary condition (BBC) with a truncated Fourier series. Two wave profiles were derived by applying the potential to the kinematic free surface boundary condition (KFSBC) and the dynamic free surface boundary condition (DFSBC). A set of nonlinear equations was represented to determine the Fourier coefficients, which were derived so that the two profiles are identical at specified phases. The set of equations was solved using Newton's method. This study proved that there is a limit to the series order, i.e., the maximum series order is N=12, and that there is a height limitation of this method which is slightly lower than the Michell theory. The reason why the other Fourier approximations are not suitable for deep water waves is discussed.

ON THE ABSOLUTE CONVERGENCE OF LACUNARY VECTOR VALUED FOURIER COEFFICIENTS SERIES

  • Rashwan, R.A.
    • Kyungpook Mathematical Journal
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    • v.27 no.2
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    • pp.173-179
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    • 1987
  • In this article the absolute convergence of lacunary Fourier Coefficients Series is studied for Hilbert space valued functions. The considered functions arc assumed to be of either the modulus of continuity or the modulus of smoothness of order l which are considered only at a fixed point in [$-{\pi},{\pi}$]. On the other hand for values in weakly sequentially complete Banach space, the lacunary Fourier coefficients series is strongly unconditionally convergent. The results obtained here are a kind of a generalization of the results due to Kandil [4].

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Genetic Diversity of Soybean Pod Shape Based on Elliptic Fourier Descriptors

  • Truong Ngon T.;Gwag Jae-Gyun;Park Yong-Jin;Lee Suk-Ha
    • KOREAN JOURNAL OF CROP SCIENCE
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    • v.50 no.1
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    • pp.60-66
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    • 2005
  • Pod shape of twenty soybean (Glycine max L. Merrill) genotypes was evaluated quantitatively by image analysis using elliptic Fourier descriptors and their principal components. The closed contour of each pod projection was extracted, and 80 elliptic Fourier coefficients were calculated for each contour. The Fourier coefficients were standardized so that they were invariant of size, rotation, shift, and chain code starting point. Then, the principal components on the standardized Fourier coefficients were evaluated. The cumulative contribution at the fifth principal component was higher than $95\%$, indicating that the first, second, third, fourth, and fifth principal components represented the aspect ratio of the pod, the location of the pod centroid, the sharpness of the two pod tips and the roundness of the base in the pod contour, respectively. Analysis of variance revealed significant genotypic differences in these principal components and seed number per pod. As the principal components for pod shape varied continuously, pod shape might be controlled by polygenes. It was concluded that principal component scores based on elliptic Fourier descriptors yield seemed to be useful in quantitative parameters not only for evaluating soybean pod shape in a soybean breeding program but also for describing pod shape for evaluating soybean germplasm.