• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.4
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• pp.639-642
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• 2012

Optical coherence tomography(OCT) can provide real-time and non-invasive subsurface imaging with ultra-high resolution of micrometer scale. However, conventional OCT systems generally have a limited imaging depth range within a depth of only 1-2 mm. To overcome the limitation, we have proposed an active surface tracking algorithm used in common-path Fourier-domain OCT system in order to extend the imaging depth range. The surface tracking algorithm based on the threshold and Savitzky-Golay filter of A-scan data was applied to real-time tracking. The algorithm has controlled a moving stage according to the sample's surface variance in real time. An OCT image obtained by the algorithm clearly show an extended imaging depth range. Consequently, the proposed algorithm demonstrated the potential for improving the conventional OCT systems with limitary depth range.

• Journal of Biomedical Engineering Research
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• v.10 no.3
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• pp.323-330
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• 1989

Large bias errors which occur during a numerical evaluation of the Rayleigh's integral is not due to the replicated source problem but due to the coincidence of singularities of the Green's function and the sampling points in Fourier domain. We found that there is no replicated source problem in evaluating the Rayleigh's integral numerically by the reason of the periodic assumption of the input sequence in Dn or by the periodic sampling of the Green's function in the Fourier domain. The wrap around error is not due to an overlap of the individual adjacent sources but berallse of the undersampling of the Green's function in the frequency domain. The replicated and overlApped one is inverse Fourier transformed Green's function rather than the source function.

• Bulletin of the Society of Naval Architects of Korea
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• v.24 no.4
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• pp.9-18
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• 1987

The hydrodynamic radiation forces acting on a ship travelling in waves have been conventionally treated by strip theories or by direct three dimensional approaches, most of which have been formulated in frequency domain. If the forward speed of a ship varies with time, or if its path is not a straight line, conventional frequency domain analysis can no more be used, and for these cases time domain analysis may be used. In this paper, formulations are made in time domain with applications to some problems the results of which are known in frequency domain. And the results of both domains are compared to show the characteristics and validity of time domain solutions. The radiation forces acting on a three dimensional body within the framework of a linear theory. If the linearity of entire system is assumed, radiation forces due to arbitrary ship motions can be expressed by the convolution integral of the arbitrary motion velocity and the so called impulse response function. Numerical calculations are done for some bodies of simple shapes and Series-60[$C_B=0.7$] ship model. For all cases, integral equation techniques with transient Green's function are used, and velocity or acceleration potentials are obtained as the solution of the integral equations. In liner systems, time domain solutions are related with frequency domain solutions by Fourier transform. Therefore time domain solutions are Fourier transformed by suitable relations and the results are compared with various frequency domain solutions, which show good agreements.

• The Journal of the Acoustical Society of Korea
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• v.15 no.4E
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• pp.53-57
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• 1996

An extension of the well-known Fourier transform is developed in this paper. It is denoted as the generalized Fourier transform(GFT), since it encompasses the Fourier transform as its special case. The first idea of this extension can be found on [1]. In the definition of the N-point discrete GFT, it first construct a passband in time which functions as a window in the time domain. An appropriate interpretation of each variables are introduced during the definition of the GFT, followed by the formal derivation of the inverse GFT. This transform pair is similar to the windowing in the frequency domain such as the subband coding technique (or filter bank approach) and could be extended to the wavelet transform.

• Proceedings of the Korea Electromagnetic Engineering Society Conference
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• 2000.11a
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• pp.29-33
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• 2000

The classical image reconstruction for stripmap SAR is based on the Fresnel approximation which utilizes deramping or chirp deconvolution in the synthetic aperture(slow-time) domain. Another approach in formulating stripmap SAR processing and imaging is based on the SAR wavefront reconsturction theory, and analysis of the SAR signal in the slow-time via the spherical wave Fourier decomposition of the radar radiation pattern. In this paper, we compare the Fresnel approximation and the wavefrong reconstruction methods using simulated stripmap SAR dada.

• Geophysics and Geophysical Exploration
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• v.17 no.3
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• pp.129-136
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• 2014

Electromagnetic (EM) methods are generally divided into frequency-domain EM (FDEM) and time-domain EM (TDEM) methods, depending on the source waveform. The FDEM and TDEM fields are mathematically related by the Fourier transformation, and the TDEM field can thus be obtained as the Fourier transformation of FDEM data. For modeling in time-domain, we can use fast frequency-domain modeling codes and then convert the results to the time domain with a suitable numerical method. Thus, frequency-to-time transformations are of interest to EM methods, which is generally attained through fast Fourier transform. However, faster frequency-to-time transformation is required for the 3D inversion of TDEM data or for the processing of vast air-borne TDEM data. The diffusion expansion method (DEM) is one of smart frequency-to-time transformation methods. In DEM, the EM field is expanded into a sequence of diffusion functions with a known frequency dependence, but with unknown diffusion-times that must be chosen based on the data to be transformed. Especially, accuracy of DEM is sensitive to the diffusion-time. In this study, we developed a method to determine the optimum range of diffusion-time values, minimizing the RMS error of the frequency-domain data approximated by the diffusion expansion. We confirmed that this method produces accurate results over a wider time range for a homogeneous half-space and two-layered model.

• Korean Journal of Optics and Photonics
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• v.22 no.2
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• pp.72-76
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• 2011

We demonstrate a k-domain linearization using a fiber Bragg grating (FBG) array for Fourier domain optical coherence tomography based on a wavelength swept laser. The k-domain linearization is carried out with an interpolation method using a FBG array with five FBGs. The measured signal-to-noise ratio from the point spread function after k-domain linearization is 12 dB improved over that of without k-domain linearization at the 1 mm depth of the sample. Clear OCT imaging of the slide glass with k-domain linearization could be obtained.

• Honam Mathematical Journal
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• v.32 no.1
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• pp.101-112
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• 2010

Using some interesting convolution, we find kernels recovering the given function f. By a slight change of this convolution, we obtain an identity filter related to the Fourier series in the discrete time domain. We also introduce some techniques to decompose an impulse into several dilated pieces in the discrete domain. The detail examples deal with specific constructions of those decompositions. Also we obtain localized moving averages from a decomposition of an impulse to make hybrid Bollinger bands, that might give various strategies for stock traders.

• Steel and Composite Structures
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• v.32 no.6
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• pp.779-793
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• 2019

The purpose of this research paper is to depict the thermomechanical interactions in transversely isotropic magneto thermoelastic solid with two temperatures and without energy dissipation in generalized LS theories of thermoelasticity. The Laplace and Fourier transform techniques have been used to find the solution of the problem. The displacement components, stress components, and conductive temperature distribution with the horizontal distance are computed in the transformed domain and further calculated in the physical domain numerically. The effect of two temperature and relaxation time are depicted graphically on the resulting quantities.

• Geophysics and Geophysical Exploration
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• v.24 no.4
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• pp.158-163
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• 2021

The frequency-domain induced polarization (IP) response based on Cole-Cole model is expressed as a simple equation in close form. However, it is difficult to compute the time-domain IP response based on Cole-Cole model or any other relaxation model because it cannot be written in closed form. In this study, using numerical experiments, we compared three numerical methods for calculating the time-domain IP response of the Cole-Cole model asymptotically: series expansion, digital linear filtering and Fourier transform. The series expansion method is inadequately accurate for certain time values and converges very slowly. A digital linear filter specially designed to calculate the time-domain IP response does not present the desired accuracy, especially at later times. The Fourier transform method can overcome the abovementioned problems and present the time-domain IP response with adequate accuracy for all time values, even though more computing time is required.