• Communications of the Korean Mathematical Society
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• v.2 no.2
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• pp.139-144
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• 1987

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.14 no.1
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• pp.35-42
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• 2010

A goal of Magnetic Resonance Imaging is reproducing a spatial map of the effective spin density from the measured Fourier coefficients of a specimen. The imaging procedure can be done by inverse Fourier transformation or backward fast Fourier transformation if the data are sampled on a regular grid in frequency space; however, it is still a challenging question how to reconstruct an image from a finite set of Fourier data on irregular points in k-space. In this paper, we describe some mathematical and numerical properties of imaging techniques from non-uniform MR data using the pseudo-inverse or the diagonal-inverse weight matrix. This note is written as an easy guide to readers interested in the non-uniform MRI techniques and it basically follows the ideas given in the paper by Greengard-Lee-Inati [10, 11].

• Journal of Ocean Engineering and Technology
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• v.28 no.2
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• pp.119-125
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• 2014

A vertical planar motion mechanism(VPMM) test was used to increase the prediction accuracy for the maneuverability of an underwater glider model. To improve the accuracy of the linear hydrodynamic coefficients, the analysis techniques of a pure heave test and pure pitch test were developed and confirmed. In this study, the added mass and damping coefficient were measured using a VPMM test. The VPMM equipment provided pure heaving and pitching motions to the underwater glider model and acquired the forces and moments using load cells. As a result, the hydrodynamic coefficients of the underwater glider could be acquired after a Fourier analysis of the forces and moments. Finally, a motion control simulation was performed for the glider control system, and the results are presented.

• The Transactions of the Korea Information Processing Society
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• v.6 no.4
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• pp.1112-1119
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• 1999

Digital watermarking is to embed imperceptible mark into image, video, audio and text data to prevent the illegal copy of multimedia data, arbitrary modification, and also illegal sales of the copes without agreement of copyright ownership. The DCT(discrete Cosine Transforms) transforms of original image is conducted in this research and these DCT coefficients are expanded by Fourier series expansion algorithm. In order to embed the imperceptible and robust watermark, the Fourier coefficients(lower frequency coefficients) can be calculated using sine and cosine function which have a complete orthogonal basis function, and the watermark is embedded into these coefficients, In the experiment, we can show robustness with respect to image distortion such as JPEG compression, bluring and adding uniform noise. The correlation coefficient are in the range from 0.5467 to 0.9507.

• Journal for History of Mathematics
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• v.26 no.2_3
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• pp.163-176
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• 2013

This study concerns Stanojevic's academic works on the $\mathfrak{L}^1$-convergence of Fourier series from 1973 to 2002. We review his academic works. Also, we briefly investigate a simple academic lineage for the researchers of $\mathfrak{L}^1$-convergence of Fourier series until 2012. First, we introduce the classical lineage of the researchers for $\mathfrak{L}^1$-convergence Fourier series in section 2. Second, we investigate the backgrounds of Stanojevic's study at Belgrade University and University of Missouri-Rolla respectively. Finally, we compare and consider the $\mathfrak{L}^1$-convergence theorems of Stanojevic's results from 1973 to 2002 successively. In addition, we compose a the simple lineage of $\mathfrak{L}^1$-convergence of Fourier series from 1973 to 2012.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.7
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• pp.3438-3454
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• 2018

In this paper, we propose a robust blind watermarking scheme for high-definition video. In the embedding process, luminance component of each frame is transformed by 2-dimensional fast Fourier transform (2D FFT). A secret key is used to generate a matrix of random numbers for the security of watermark information. The matrix is transformed by inverse steerable pyramid transform (SPT). We embed the watermark into the low and mid-frequency of 2D FFT coefficients with the transformed matrix. In the extraction process, the 2D FFT coefficients of each frame and the transformed matrix are transformed by SPT respectively, to produce two oriented sub-bands. We extract the watermark from each frame by cross-correlating two oriented sub-bands. If a video is degraded by some attacks, the watermarks of frames contain some errors. Thus, we use an ensemble position-based error correcting algorithm to estimate the errors and correct them. The experimental results show that the proposed watermarking algorithm is imperceptible and moreover is robust against various attacks. After embedding 64 bits of watermark into each frame, the average peak signal-to-noise ratio between original frames and embedded frames is 45.7 dB.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.29 no.6
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• pp.1393-1401
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• 2019

Recently as voice authentication function is installed in the system, it is becoming more important to accurately authenticate speakers. Accordingly, a model for verifying speakers in various ways has been suggested. In this paper, we propose a new method for verifying speaker verification using a Short-time Fourier Transform(STFT). Unlike the existing Mel-Frequency Cepstrum Coefficients(MFCC) extraction method, we used window function with overlap parameter of around 66.1%. In this case, the speech characteristics of the speaker with the temporal characteristics are studied using a deep running model called RNN (Recurrent Neural Network) with LSTM cell. The accuracy of proposed model is around 92.8% and approximately 5.5% higher than that of the existing speaker certification model.

• Bulletin of the Korean Mathematical Society
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• v.21 no.2
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• pp.127-135
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• 1984

In this paper, we find the Fourier series of X(t, .omega.).mem. $L^{2}$$_{s.a.p.}$ and the Parseval relation of X(t, .omega.).mem. $L^{2}$$_{s.a.p.}$. In section 2, we investigate some basic properties of X(t, .omega.).mem. $L^{2}$$_{s.a.p.}$ In section 3, we show that the mean of X(t, .omega.).mem. $L^{2}$$_{s.a.p.}$ exists and in section 4, after showing the existence of Fourier exponents and Fourier coefficients of X(t, .omega.).mem. $L^{2}$$_{s.a.p.}$. we give the Parseval relation of X(t, .omega.).mem. $L^{2}$$_{s.a.p.}$. For convenience we will denote X(t, .omega.) as X(t) in what follows.hat follows.

• Journal of Applied Reliability
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• v.16 no.2
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• pp.110-117
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• 2016

Purpose: Biswas and Sarkar [11] found the availability of a system maintained through several imperfect repairs before a replacement is allowed. However they missed a part of coefficients in the integration. This paper corrects the erratum of Biswas and Sarkar [11] and performs the reliability analysis incorporating the optimal number of imperfect repairs. Methods: To find the singularities and residues of the suitable complex-valued function for the availability, the computer package Matlab is used. Also the performance measures are calculated by defining and assigning costs. Results: The accurate availability functions with respect to the numbers of imperfect repairs and the optimal number of imperfect repairs before a replacement are obtained. Conclusion: The reliability for a system under imperfect repair before a replacement is analyzed using Fourier transform technique.

• Journal of KSNVE
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• v.4 no.2
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• pp.137-146
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• 1994

An analytical method for linear free vibration of fully liquid-filled circular cylindrical shell with various boundary conditions is developed by the Fourier series expansion based on the Stokes' transformation. A set of modal displacement functions and their derivatives of a circular cylindrical shell is substituted into the Sanders' shell equations in order to explicitily represent the Fourier coefficients as functions of the end point displacements, forces, and moments. For the vibration relevant to the liquid motion, the velocity potential of liquid is assumed as a sum of linear combination of suitable harmonic functions in the axial directions. The unknown parameter of the velocity potential is selected to satisfy the boundary condition along the wetted shell surface. An explicit expression of the natural frequency equation can be obtained for any kind of classical boundary conditions. The natural frequencies of the liquid-filled cylindrical shells with the clamped-free, the clamped-clamped, and the simply supported-simply supported boundary conditions examined in the previous works, are obtained by the analytical method. The results are compared with the previous works, and excellent agreement is found for the natural frequencies of the shells.