• Journal of KSNVE
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• v.6 no.6
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• pp.771-779
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• 1996

In this paper, 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 method of stationary potential energy is used to obtain the modal displacements of a plate. To enhance the flexibility of the double Fourier sine series, Lagrangian multipliers are utilized to match the geometric boundary conditions, and Stokes' transformation is used to handle the displacements that are not satisfied by the double Fourier sine series. The frequency parameters and mode shapes obtained by the present method are compared with those obtained by MSC/NASTRAN and other analysis.

• IEIE Transactions on Smart Processing and Computing
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• v.4 no.2
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• pp.103-109
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• 2015

In this paper, a novel method for the classification of term and preterm birth is proposed based on time-frequency analysis of electrohysterogram (EHG) using multivariate empirical mode decomposition (MEMD). EHG is a promising study for preterm birth prediction, because it is low-cost and accurate compared to other preterm birth prediction methods, such as tocodynamometry (TOCO). Previous studies on preterm birth prediction applied prefilterings based on Fourier analysis of an EHG, followed by feature extraction and classification, even though Fourier analysis is suboptimal to biomedical signals, such as EHG, because of its nonlinearity and nonstationarity. Therefore, the proposed method applies prefiltering based on MEMD instead of Fourier-based prefilters before extracting the sample entropy feature and classifying the term and preterm birth groups. For the evaluation, the Physionet term-preterm EHG database was used where the proposed method and Fourier prefiltering-based method were adopted for comparative study. The result showed that the area under curve (AUC) of the receiver operating characteristic (ROC) was increased by 0.0351 when MEMD was used instead of the Fourier-based prefilter.

• 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.

• Korean Journal of Optics and Photonics
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• v.8 no.3
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• pp.199-203
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• 1997

Fine displacement of spherical suface was detected and analyzed by Twyman-Green interferometer and the interferogram analysis using Fourier transform method. The surface profile was obtained from single interferogram by introducing the carrier freguency to the interferogram. The interferogram was processed in the spatial frequency domain by fast Fourier transform, and the phase distribution was obtained by inverse Fourier transform. The 3-dimensional distribution for the surface displacement was obtained. It was compared with the calculated surface displacement and the error was less than λ/10.

• Journal for History of Mathematics
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• v.27 no.4
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• pp.285-297
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• 2014

G. H. Hardy laid the foundation of classical studies on double Fourier series at the beginning of the 20th century. In this paper we are concerned not only with Fourier series but more generally with trigonometric series. We consider Norlund means and Cesaro summation method for double Fourier Series. In section 2, we investigate the classical results on the summability and the convergence of double Fourier series from G. H. Hardy to P. Sjolin in the mid-20th century. This study concerns with the $L^1(T^2)$-convergence of double Fourier series fundamentally. In conclusion, there are the features of the classical results by comparing and reinterpreting the theorems about double Fourier series mutually.

• The Journal of Korean Institute for Practical Engineering Education
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• v.2 no.2
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• pp.36-41
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• 2010

Many references are available in the area of Fourier transformation. But some differences are found in the mathematical expressions provided in the references. These circumstances prohibit beginners from understanding and using Fourier transformation method. In this paper, relating mathematical expressions are epitomized and some numerical results are compared and interpreted to understand Fourier transformation. Fourier transformation results are displayed for representative input signals and some characteristics are summarized.

• Journal of the Optical Society of Korea
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• v.16 no.3
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• pp.196-202
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• 2012

We observe that the transmission and reflection efficiencies of a one-dimensional metallic grating under transverse-magnetic illumination calculated using the Fourier modal method (FMM) with the Fourier factorization rules have peculiar fluctuations, albeit small in magnitude, as the number of field harmonics increases. It is shown that when the number of Fourier terms for the electromagnetic field is increased from that in the conventional FMM, the fluctuations due to non-convergent highly evanescent eigenmodes can be eliminated. Our examination reveals that the fluctuations originate from the Gibbs phenomenon inherent in the Fourier-series representation of a permittivity function with discontinuities, and from non-convergence of highly evanescent internal Bloch eigenmodes.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.10 s.181
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• pp.2560-2567
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• 2000

When spatially dense velocity distribution is measured by a scanning laser Doppler vibrometer, the Fourier transform method provides the real and imaginary parts of the mode shapes in the form of a polynomial. However the Fourier transform method is often impractical because the independent decomposition property of cosine and sine components into real and imaginary parts, respectively, does not hold due to the leakage problem which commonly occurs in the Fourier transform of harmonic signals. To deal with this problem, a Hilbert transform method is newly proposed in this article. The proposed method is free from the leakage problem and relatively robust to the scanning error. A simulation example is provided to verify the effectiveness of this method.

• Journal of the Korean Institute of Telematics and Electronics C
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• v.35C no.8
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• pp.60-67
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• 1998

We studied the effects of fractional fourier transform in face recognition, in which only the amplitude spectra of transformed facial images were used.We used two recently developed face recognition methods, the most effective feature (MEF) method (i.e., eigenface method) and most discriminating feature (MDF) method, and the effects of th etransform for th etwo methods were consistent. We confirmed that the recognition rate by the use of MDF method is better than that consistent. We confirmed that the recognition rate by the use of MDF method is better than that by MEF regardless of the order to transform, these methods provided slightly better results when the order was 1 than for any other order values. Only when the order was close to 1, the recognition rates were robust to the shift of the input images, and the trend that the recognition rates decreased as the input size varied was independent of the order. From these results, we fond that it is most advantageous to use the amplitude spectra of the conventional fourier transform whose order is 1.

• Proceedings of the KSME Conference
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• 2000.04a
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• pp.420-425
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• 2000

When spatially dense velocity distribution is measured by a scanning laser Doppler vibrometer, the Fourier transform method provides the real and imaginary parts of the mode shapes in the form of a polynomial. However the Fourier transform method is often impractical because the independent decomposition property of cosine and sine components into real and imaginary parts, respectively, does not hold due to the leakage problem which commonly occurs in the Fourier transform of harmonic signals. To deal with this problem, a Hilbert transform method is newly proposed in this article. The proposed method is free from the leakage problem and relatively robust to tire scanning error. A simulation example is provided to verify the effectiveness of this method.