• 대한수학회보
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• 제35권2호
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• pp.345-362
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• 1998

We introduce and anlyze a naturally parallelizable frequency-domain method for parabolic problems with a Neumann boundary condition. After taking the Fourier transformation of given equations in the space-time domain into the space-frequency domain, we solve an indefinite, complex elliptic problem for each frequency. Fourier inversion will then recover the solution of the original problem in the space-time domain. Existence and uniqueness of a solution of the transformed problem corresponding to each frequency is established. Fourier invertibility of the solution in the frequency-domain is also examined. Error estimates for a finite element approximation to solutions fo transformed problems and full error estimates for solving the given problem using a discrete Fourier inverse transform are given.

• 대한수학회보
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• 제39권4호
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• pp.589-606
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• 2002

We introduce and analyze a frequency-domain method for parabolic partial differential equations. The method is naturally parallelizable. After taking the Fourier transformation of given equations in the space-time domain into the space-frequency domain, we propose to solve an indefinite, complex elliptic problem for each frequency. Fourier inversion will then recover the solution in the space-time domain. Existence and uniqueness as well as error estimates are given. Fourier invertibility is also examined. Numerical experiments are presented.

• 호남수학학술지
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• 제38권3호
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• pp.613-623
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• 2016

As a generalization of the Fourier transform, the fractional Fourier transform plays an important role both in theory and in applications of signal processing. We present a new approach to reach a uniform sampling theorem in the shift-invariant spaces associated with the fractional Fourier transform domain.

• 전자공학회논문지SC
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• 제45권1호
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• pp.25-30
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• 2008

본 논문에서는 상용 고휘도 백색광 LED 및 CCD 어레이 검파기를 이용하여 Fourier-domain 방식의 광 계측기를 구현하였다. 제안된 기술의 축 방향 측정 거리 범위는 $125{\mu}m$이고, 축 방향 분해능은 $1.24{\mu}m$이다. 기존 시스템이 고가의 광대역 광원을 사용하면서도 분해능이 수 ${\mu}m$ 이상인 것에 비추어 볼 때, 본 시스템은 저가의 상용 LED와 CCD 어레이 검파기를 사용하여 구현되므로 소형이며 가격적인 면에서 유리하면서도 높은 분해능을 얻을 수 있다.

• Journal of Mechanical Science and Technology
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• 제15권2호
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• pp.232-238
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• 2001

Fast Fourier Transformation is employed to convert the head variation of a pipeline in the time domain to the amplitude of the frequency domain. Applying method of characteristics to a pipeline provides a significant frequency range for a surge introduced from the valve modulation. Inverse Fast Fourier Transformation and a Finite Impulse Response Filter can be used to remove any possible noise existing from the significant frequency range of an unsteady condition. A filtered signal shows higher potential for the inverse calculation of leakage detection than the noise-added signal does. The respective performances of Inverse Fast Fourier Transformation and a Finite Impulse Response Filter are compared in terms of leakage detection capability. Characteristics of the frequency range for multiple leakages were investigated to validate the effectiveness of the noise control method in the frequency domain.

• 한국생산제조학회지
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• 제19권3호
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• pp.407-413
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• 2010

This paper reports on the research which analyzes acoustic signals acquired in progressive compressing, hole blanking, and burr compacting process. An acoustic sensor was set on the bed of hydraulic press. Acoustic signal is generated from progressive stamping process. First the signal acquired from the unit process; compressing, blanking or compacting, is studied by Fourier Transform and Short Time Fourier Transform. The blanking process emitted ultrasonic signal with more than 20kHz, but the compressing and compacting processes emitted acoustic signals with lower than 10kHz. The combined signals periodically acquired right after the tool grinding were then analyzed. 70-80kHz signals appeared in time-frequency domain, but not in the frequency domain, the magnitude of which was related to the tool wear. Short Time Fourier Transform made up for the Fourier Transform in analyzing the emitted signal for stamping process in the ultrasonic domain.

• Journal of information and communication convergence engineering
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• 제8권3호
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• pp.312-316
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• 2010

Conformal mapping has been a familiar tool of science and engineering for generations. The methods of numerical mapping are usually classified into those which construct the map from standard domain such as the unit disk onto the 'problem domain', and those which construct the map in the reverse direction. We treat numerical conformal mapping from the unit disk onto the Jordan regions as the problem domain in this paper. The traditional standard methods of this type are based on Theodorsen integral equation. Wegmann's method is well known as a Newton-like efficient one for solving Theodorsen equation. An improved method for convergence by applying low frequency pass filter to the Wegmann's method was proposed. In this paper we propose an effective algorithm for numerical conformal mapping based on the improved method. This algorithm is able to determine the discrete numbers and initial values automatically in accordance with the given region and the required accuracy. This results come from analyzing the shape of given domain as seen in the Fourier Transform.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제11권11호
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• pp.5377-5391
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• 2017

In this paper, we propose a new scheme to suppress the narrowband interference (NBI) in OFDM-based systems. The scheme utilizes code division multiple access (CDMA) and weighted-type fractional Fourier transform (WFRFT) domain preprocessing technologies. Through setting the WFRFT order, the scheme can switch into a single carrier (SC) or a multi-carrier (MC) frequency division multiple access block transmission system. The residual NBI can be eliminated to the maximum extent when the WFRFT order is selected properly. Final simulation results show that the proposed system can outperform MC and SC with CDMA and frequency domain preprocessing in terms of the narrowband interference suppression.

• East Asian mathematical journal
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• 제26권1호
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• pp.105-113
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• 2010

In the spectral analysis, Fourier coeffcients are very important to give informations for the original signal f on a finite domain, because they recover f. Also Fourier analysis has extension to wavelet analysis for the whole space R. Various kinds of reconstruction theorems are main subject to analyze signal function f in the field of wavelet analysis. In this paper, we will present a new reconstruction theorem of functions in $L^1(R)$ using a nonharmonic Fourier series. When we construct this series, we have used dyadic subdivision schemes.

• 한국철도학회논문집
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• 제9권2호
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• pp.187-192
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• 2006

The regularity of railway track alignment is a crucial component fur maintaining travel safety and the smoothness of passenger ride. The conventional spectral analysis has been considered to estimate the severity of the track irregularity from measured data. The time domain data used to be changed into the frequency domain by Fourier transform. Because the measuring points can be regarded as the time points, the spatial-frequency can be introduced instead of the time-frequency. Although FFT(Fast Fourier Transform) and/or PSD(Power Spectral Density) function could provide fairly localized information within frequency domain, but chronical configurations of data could be missed. In this study, we attempt to apply the Morlet wavelet transform for the purpose of a frequency-time-domain analysis rather than a frequency-domain analysis. The applicability of wavelet transform is examined for the estimation of the track irregularity with real measured track data on the section of Kyoung-bu line by EM-120 measuring vehicle. It is shown that the wavelet transform can be an effective tool to manage the track irregularity.