• Journal of applied mathematics & informatics
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• v.4 no.1
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• pp.39-46
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• 1997

Given to be the $m^{th}$ correlation coefficient of the Rudin-Shapiro polynomials of degrees $2^n-1$, $$\mid$a_m$\mid$ \leq C(2^n)^{\frac{3}{4}}$ and there exists $\kappa \neq 0$ such that $$\mid$a_{\kappa}$\mid$ ＞D(2^n)^{0.73}$ (C and D are universal constants). Here we show that the 0.73 is optimal in the upper vound case.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2001.10a
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• pp.169-173
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• 2001

This study presents the results of decoupling of free decay roll test data by discrete wavelet transform. Free roll decay test was performed to decide the coefficients of damping terms in equation of motion. During the experiment, a slight yaw motion was found while the model was in the free roll decay motion. Discrete wavelet transform was applied to the signal to extract the pure roll motion. The results were compared to those of the Fourier transform. DWT was able to decouple the two signals efficiently while the Fourier transform was not.

• Journal of the Korean Mathematical Society
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• v.52 no.2
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• pp.333-347
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• 2015

In this paper, by using the modular forms of weight nk ($2{\leq}n{\in}\mathbb{N}$ and $k{\in}\mathbb{Z}$), we construct a formula which generates modular forms of weight 2nk+4. This formula consist of some known results in [14] and [4]. Moreover, we obtain Fourier expansion of these modular forms. We also give some properties of an operator related to the derivative formula. Finally, by using the function $j_4$, we obtain the Fourier coefficients of modular forms with weight 4.

• 제어로봇시스템학회:학술대회논문집
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• 1990.10b
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• pp.1145-1149
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• 1990

This paper proposes a numerical method for redundant manipulators using predetermined optimal resolution. In order to obtain optimal joint trajectories, it is desirable to formulate redundancy resolution as an optimization problem having an integral cost criterion. We predetermine the trajectories of redundant joints in terms of the Nth partial sum of the Fourier series, which lead to the solution in the desirable homotopy class. Then optimal coefficients of the Fourier series, which yield the optimal solution within the predetermined class, are searched by the Powell's method. The proposed method is applied to a 3-link planar manipulator for cyclic tasks in Cartesian space. As the results, we can obtain the optimal solution in the desirable homotopy class without topological liftings of the solution. To show the validity of the proposed method, we analyze both optimal and extremal solutions by the Fast Fourier Transform (FFT) and discuss joint trajectories on the phase plane.

• 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.

• Transactions of the Korean Society of Automotive Engineers
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• v.3 no.2
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• pp.42-50
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• 1995

This paper proposes a new method to investigate combustion phenomena using the variation of crankshaft speed, From the idea that the variation of crankshaft speed contains the information of combustion, the energy method is applied as a single degree of freedom. Through the comparison of measured and calculated crankshaft speed, the proposed energy model is proved to be effective. When the crankshaft speed is used in the energy equation, filtering of the speed is required. The frequency components of cylinder pressure are analyzed and the coefficients of Fourier series above the twelfth frequency of engine speed are considered as a noise. As an example of application of this research, some combustion analyses like mean effective pressure, heat release rate, and misfire detection were carried out.

• Food Science and Biotechnology
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• v.18 no.5
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• pp.1199-1203
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• 2009

Melamine is a chemical intermediate to manufacture amino resins and plastics, which cannot be used as food additive since it can cause kidney stones. A qualitative determination method of melamine residue in powdered and liquid milk was developed using Fourier transform infrared (FTIR) spectroscopic technique. The calibration sets consisted of 21 standard melamine solutions, in which 1% trichloroacetic acid aqueous solution and acetonitrile (3:1, v/v) were used as solvent. The model was validated using 10 standard melamine solutions which were unused to build up the calibration set. Infrared (IR) absorbance peaks specific to almost all chemical groups in melamine molecule were shown in the spectral range between 1,100 and 1,800/cm. Combined partial least squares (PLS)-$2^{nd}$ derivative calibration model coupled with mean centering (MC) mathematical enhancement showed the highest correlation coefficients ($R^2$>0.99). In brief, the FTIR technique can be used for quantitative analysis of melamine in milk samples.

• Journal for History of Mathematics
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• v.19 no.2
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• pp.115-124
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• 2006

Functions of bounded variation were discovered by Jordan in 1881 while working out the proof of Dirichlet concerning the convergence of Fourier series. Here, we investigate Waterman's study with respect to bounded variation and its application on a closed bounded interval. The value of his study is whether Dirichlet-Jordan theorem holds in which function classes or not and summability method is what modifies its Fourier coefficients to make resulting series converge to the associated function. We have a view that the directions of future research with respect to bounded variation are two things; one is to find the function spaces which are larger than HBV and smaller than ${\phi}BV$, and the other is to find a fields of applications.

• Journal of the Optical Society of Korea
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• v.3 no.1
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• pp.23-26
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• 1999

A simple technique to measure electro-optic coefficients has been developed. It is based on rotating analyzer polarimetry. With a coaxial configuration of the optically active polarizing devices, the synchronously digitized signals are Fourier analyzed to quantitatively determine the elliptical polarization of light and, hence, the electric field induced birefringence. This technique has the advantage that it does not require waveguiding, and since it is improved from the crossed polarizer method it measures the phase retardation directly. It has been applied for the precise determination of electro-optic coefficients of uniaxial LiNbO3 single crystals. The excellent agreeement with reported values confirms its usefulness toward accurate characterization of electro-optic coefficients of unknown specimens.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.37 no.5
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• pp.9-20
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• 2000

In this paper we compare two frequency domain digital watermarking methods for digital Images, namely DCT(Discrete Cosine Transform) based and DFT(Discrete Fourier Transform) based methods. Unlike DCT coefficients, which always have real values, DFT coefficients normally have complex values Therefore, the DFT coefficients have amplitude and phase components Among them, the phase components are known to carry more Important information for the Images. So, we insert the watermark to the phase of the DFT coefficients only This DFT watermarking method is compared with the conventional DCT based watermarking method for the object-based watermarking problem. Experimental results show that the DFT-phase based method IS more robust to general Image processing attacks including resize, lossy compression(JPEG), blurring and median filtering. On the other hand, the DCT based method is more robust to the malicious attack which inserts different watermarks.