• Research in Mathematical Education
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• v.13 no.2
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• pp.103-108
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• 2009

We present the thoughts behind a course combining the subjects of differential equations and infinite series. The key point is how to connect the two topics in a course with a natural flow.

• Nuclear Engineering and Technology
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• v.25 no.1
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• pp.148-153
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• 1993

A fifth-order Fourier series technique is applied in Core Operating Limit Supervisory System (COLSS) to construct the on-line core average axial power shape from in-core detector signals because of its simplicity and fast computation. Such a synthesizing accuracy depends on number of Fourier series modes and axial boundary conditions. COLSS currently uses the five-mode Fourier series technique which utilizes the five axially located fixed in-core detector signals and a constant axial boundary condition. Therefore, the constant axial boundary condition should be appropriately chosen based on the evaluation of its effect on the accuracy of the on-line calculations. The four cases of axial buckling (0.75, 0.8, 0.9 and 1.0) were examined for Yonggwang Nuclear Units 3&4 as the axial boundary conditions in this paper. The core average axial power shapes and the operating margins were compared for each case to determine the optimal constant axial buckling. The axial buckling of 0.9 was found to be the optimal value.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.55 no.7
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• pp.265-272
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• 2006

This paper describes a method of parameter estimation of time series data using discrete Fourier transform(DFT). DFT have been mainly used to precisely and rapidly obtain the frequency of a signal. In a dynamic system, a real part of a mode used to learn damping characteristics is a more important factor than the frequency of the mode. The parameter estimation method of this paper can directly estimate modes and parameters, indicating the characteristics of a dynamic system, on the basis of the Fourier transform of the time series data. Real part of a mode estimates by subtracting a frequency of the Fourier spectrum corresponding to 0.707 of a magnitude of the peak spectrum from a peak frequency, or subtracting a frequency of the power spectrum corresponding to 0.5 of the peak power spectrum from a peak frequency, or comparing the Fourier(power) spectrum ratio. Also, the residue and phase of time signal calculate by simple equation with the real part of the mode and the power spectrum that have been calculated. Accordingly, the proposed algorithm is advantageous in that it can estimate parameters of the system through a single DFT without repeatedly calculating a DFT, thus shortening the time required to estimate the parameters.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.351-358
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• 2007

For an entire function f whose Fourier transform has a compact support confined to $[-{\pi},\;{\pi}]$ and restriction to ${\mathbb{R}}$ belongs to $L^2{\mathbb{R}}$, we derive a nonuniform sampling theorem of Lagrange interpolation type with sampling points ${\lambda}_n{\in}{\mathbb{R}},\;n{\in}{\mathbb{Z}}$, under the condition that $$\frac{lim\;sup}{n{\rightarrow}{\infty}}|{\lambda}_n-n|<\frac {1}{4}$.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.11a
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• pp.406-412
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• 1996

Optimal trajectory for a robot manipulator minimizing actuator torques or energy consumption in a fixed traveling time is obtained in the presence of obstacles. All joint displacements are represented in finite terms of Fourier cosine series and the coefficients of the series are obtained optimally by nonlinear programming. Thus, the geometric path need not be prespecified and the full dynamic model is employed. To avoid the obstacles, the concept of penalty area is newly introduced and this penalty area is included in the performance index with an appropriate weighting coefficient. This optimal trajectory will be useful as a geometric path in the minimum-time trajectory planning problem.

• Journal of the Korea Society of Computer and Information
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• v.28 no.4
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• pp.1-11
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• 2023

In this paper, instead of using recurrent neural network, we compare a classification performance of time series imaging algorithms using convolution neural network. There are traditional algorithms that imaging time series data (e.g. GAF(Gramian Angular Field), MTF(Markov Transition Field), RP(Recurrence Plot)) in TSC(Time Series Classification) community. Furthermore, we compare STFT(Short Time Fourier Transform) algorithm that can acquire spectrogram that visualize feature of voice data. We experiment CNN's performance by adjusting hyper parameters of imaging algorithms. When evaluate with GunPoint dataset in UCR archive, STFT(Short-Time Fourier transform) has higher accuracy than other algorithms. GAF has 98~99% accuracy either, but there is a disadvantage that size of image is massive.

• Journal of Magnetics
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• v.18 no.2
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• pp.130-134
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• 2013

Most electrical machines like motor, generator and transformer are symmetric in terms of magnetic field distribution and mechanical structure. In order to analyze these problems effectively, many coupling techniques have been introduced. This paper deals with a coupling scheme for open boundary problem of symmetric and periodic structure. It couples an analytical solution of Fourier series expansion with the standard finite element method. The analytical solution is derived for the magnetic field in the outside of the boundary, and the finite element method is for the magnetic field in the inside with source current and magnetic materials. The main advantage of the proposed method is that it retains sparsity and symmetry of system matrix like the standard FEM and it can also be easily applied to symmetric and periodic problems. Also, unknowns of finite elements at the boundary are coupled with Fourier series coefficients. The boundary conditions are used to derive a coupled system equation expressed in matrix form. The proposed algorithm is validated using a test model of a bush bar for the power supply. And the each result is compared with analytical solution respectively.

• Proceedings of the KIEE Conference
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• 1998.07a
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• pp.64-66
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• 1998

This paper presents a new efficient method for transient analysis in magnetodynamic systems of linear eddy current problems. This mehtod employs the Fourier transform and the high-order frequency sensitivity of harmonic finite element method. By taking into account the time-constant of magnetodynamic system, the Fourier integral of continuous frequency is converted into the Fourier series of discrete frequency. And with the results of Fourier series expansion of converted input wave form, the responses of each sinusoids is superposed to give the total response of the magnetodynamic systems. But, if the frequency band of input wave form is broad, it takes long computational time since all responses for each sinusoids must be calculated. Therefore, the high-order frequency sensitivity method is employed to estimate the response variation to frequency. The proposed algorithm is applied to an induction heating system to validate its numerical efficiency.

• The Journal of the Acoustical Society of Korea
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• v.18 no.7
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• pp.39-44
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• 1999

An analysis of the frequency parameters and vibrational modes is described for a rectangular plate. Double Fourier sine series is used as a modal displacement functions of a rectangular plate and applied to the free vibration analysis of a rectangular plate under various boundary conditions. The frequency parameters obtained by the double Fourier sine series method are compared with those obtained by the theory of finite element method and Ritz method. Frequency parameters are presented for the various aspect ratios for plate. The first four modal shapes for the rectangular plate under various boundary conditions are accurately described.