• Journal of applied mathematics & informatics
• /
• v.27 no.1_2
• /
• pp.419-426
• /
• 2009

In expansion of function by special basis functions, properties of expansion kernel are very important. In the Fourier series, the series are expressed by the convolution with Dirichlet kernel. We investigate some of properties of kernel in wavelet expansions both in one and higher dimensions.

• Bulletin of the Korean Chemical Society
• /
• v.16 no.11
• /
• pp.1089-1093
• /
• 1995

The p-xylyl radical has been produced in a jet from the precursor p-xylene with a corona excited supersonic expansion. Rotationally cooled vibronic emission spectra in the transition of 12A2→12B2 of the p-xylyl radical have been recorded using a Fourier transform spectrometer. The spectra were analyzed on the basis of the known vibrational frequencies and the bandshapes given by the rotational selection rules.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.10 no.1
• /
• pp.31-37
• /
• 1985

An interesting area of application which makes use of the unique features of the walsh series is that on non-linear stochastic problems. In particular, some success has been obtained in improving the efficiency of signal detection for those transducers which are essentially non-linear in operation. The set of harmonically-related nonorthogonal triangle waves is shown to form a basis apanning the same function space representable by fourier(trigonometric) series. A method for generating nonorthogonal bases for signal representation is presented tailor-made basis function can be used for specific purposes. Fundamental proofs of the basis properties of the representation are examined along with examples illustrating the techniques and computer simulation.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
• /
• v.13 no.9
• /
• pp.937-946
• /
• 2002

In this paper, we present a stable solution of the transient electromagnetic scattering from the conducting objects. This method does not utilize the conventional marching-on in time (MOT) solution. Instead we solve the time domain integral equation by expressing the transient behavior of the induced current in terms of weighted Laguerre polynomials. By using this basis functions for the temporal variation, the time derivative in the integral equation can be handled analytically. Since these temporal basis functions converge to zero as time progresses, the transient response of the induced current does not have a late time oscillation. To show the validity of the proposed method, we solve a time domain electric feld integral equation and compare the results of MOT, Mie solution, and the inverse discrete Fourier transform (IDFT) of the solution obtained in the frequency domain.

• ETRI Journal
• /
• v.41 no.3
• /
• pp.316-325
• /
• 2019

Accurate suppressive jamming is a prominent problem faced by radar equipment. It is difficult to solve signal detection problems for extremely low signal to noise ratios using traditional signal processing methods. In this study, a joint sensing dictionary based compressed sensing and adaptive iterative optimization algorithm is proposed to counter suppressive jamming in information domain. Prior information of the linear frequency modulation (LFM) and suppressive jamming signals are fully used by constructing a joint sensing dictionary. The jamming sensing dictionary is further adaptively optimized to perfectly match actual jamming signals. Finally, through the precise reconstruction of the jamming signal, high detection precision of the original LFM signal is realized. The construction of sensing dictionary adopts the Pei type fast fractional Fourier decomposition method, which serves as an efficient basis for the LFM signal. The proposed adaptive iterative optimization algorithm can solve grid mismatch problems brought on by undetermined signals and quickly achieve higher detection precision. The simulation results clearly show the effectiveness of the method.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.10 no.4
• /
• pp.758-763
• /
• 2006

In various fields of basic science and engineering, in order to present signals and systems exactly and acquire useful information from spatial and timely changes, many researches have been processed. In these methods, the Fourier transform which represents signal as the combination of the frequency component has been applied to the most fields. But as transform not to consider time information, the Fourier transform has its limitations of application. To overcome this problem, a variety of methods including the wavelet transform have been proposed. As transform to represent signal by using the changing window, according to scale parameter in time-scale domain, the wavelet transform is capable of multiresolution analysis and defines various functions according to the application environments. In this paper, to detect features of signal we analyzed wavelet the spectrum by using the basis function of the fourier transform.

• Journal of KSNVE
• /
• v.4 no.2
• /
• pp.163-175
• /
• 1994

An analytical method for nautral frequencies of a partially liquid- filled circular cylindrical shell with various boundary conditions is developed by means of the Stokes's transformation and Fourier series expansion on the basis of Sanders' shell equation. The liquid-shell coupled system is divided into two regions for convenient formulation. One is the empty shell region in which the Sanders' shell equations are formulated without the lipuid effect, the other is wetted shell region in which the shell equations are formulated with consideration of the liquid dynamic effect. The shell equations for each regions are combined by the geometry and the force continuities at the junction of the two regions. 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 axial direction. The unknown parameters are selected to satisfy the boundary condition along the wetted shell surface. The natural frequencies of the liquid filled cylindraical shells with the clamped- free and the clamped-clamped boundary conditions examined in the previous works, are obtained by this analytical method. The results are compared with the previous works, and excllent agreement is found for the natural frequencies of the shells.

• Current Optics and Photonics
• /
• v.2 no.2
• /
• pp.165-171
• /
• 2018

Fourier ptychographic microscopy (FPM) is a recently proposed computational imaging method that achieves both high resolution (HR) and wide field of view. In the FPM framework, a series of low-resolution (LR) images at different illumination angles is used for high-resolution image reconstruction. On the basis of previous research, image noise can significantly degrade the FPM reconstruction result. Since the captured LR images contain a lot of dark-field images with low signal-to-noise ratio, it is very important to apply a noise-reduction process to the FPM raw dataset. However, the thresholding method commonly used for the FPM data preprocessing cannot separate signals from background noise effectively. In this work, we propose an improved thresholding method that provides a reliable background-noise threshold for noise reduction. Experimental results show that the proposed method is more efficient and robust than the conventional thresholding method.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.8 no.5
• /
• pp.408-415
• /
• 1984

The stress state of orthotropic cylindrical shells subjected to localized loads is considered. The governing equations for orthotropic cylindrical shells are derived on the basis of the Morley-Koiter's isotropic shell theory. It is assumed here that the material has a special orthotropy. Solutions are obtained by the Bijlaard's method in the from of double Fourier series. Numerical examples are presented for cylindrical shells having various orthotropic material properties and shell geometries.

• Journal of applied mathematics & informatics
• /
• v.27 no.5_6
• /
• pp.1017-1031
• /
• 2009

The problem of interaction of surface water waves by small undulation at the bottom of a laterally unbounded sea is treated on the basis of linear water wave theory for both normal and oblique incidences. Perturbation analysis is employed to obtain the first order corrections to the reflection and transmission coefficients in terms of integrals involving the shape function c(x) representing the bottom undulation. Fourier transform method and residue theorem are applied to obtain these coefficients. As an example, a patch of sinusoidal ripples is considered in both the cases as the shape function. The principal conclusion is that the reflection coefficient is oscillatory in the ratio of twice the surface wave number to the wave number of the ripples. In particular, there is a Bragg resonance between the surface waves and the ripples, which is associated with high reflection of incident wave energy. The theoretical observations are validated computationally.