• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.19 no.9
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• pp.968-977
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• 2008

In this paper, an analysis of TE-wave scattering from transversal-shifted tandem slits using fourier transform analysis and Wiener-Hopf technique are derived and the electrical performances have been compared with a commercially availabel software. In Fourier transform analysis, it is shown that a fast-convergent series solution can be obtained when the distance between the slits is very narrow, while in Wiener-Hopf technique, it is found that the highly-accurate approximation can be obtained when the gap between the slits becomes wider. In addition, this paper has dealt with a good agreement between two analytical solutions.

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.105-115
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• 2021

Generalized pseudo-differential operators (PDO) involving fractional Fourier transform associate with the symbol a(x, y) whose derivatives satisfy certain growth condition is defined. The product of two generalized pseudo-differential operators is shown to be a generalized pseudo-differential operator.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1101-1121
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• 2008

One proposes an approach to fractional Fourier's transform, or Fourier's transform of fractional order, which applies to functions which are fractional differentiable but are not necessarily differentiable, in such a manner that they cannot be analyzed by using the so-called Caputo-Djrbashian fractional derivative. Firstly, as a preliminary, one defines fractional sine and cosine functions, therefore one obtains Fourier's series of fractional order. Then one defines the fractional Fourier's transform. The main properties of this fractal transformation are exhibited, the Parseval equation is obtained as well as the fractional Fourier inversion theorem. The prospect of application for this new tool is the spectral density analysis of signals, in signal processing, and the analysis of some partial differential equations of fractional order.

• Proceedings of the Korean Geotechical Society Conference
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• 2003.03a
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• pp.249-256
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• 2003

To investigate the safety and stability of the concrete lining, numerous studies have been conducted over the years and several methods have been developed. Most signal processing method of NDT techniques has based on the Fourier analysis. However, the application of Fourier analysis to analyze recorded signal shows results only in frequency domain, it is not enough to analyze transient waves precisely. In this study, a new NDT technique .using the wavelet theory was employed for the analysis of non-stationary wave propagation induced by mechanical impact in the concrete lining. The wavelet transform of transient signals provides a method for mapping the frequency spectrum as a function of time. To verify the availability of wavelet transform as a time- frequency analysis tool, model experiments have been conducted on the concrete lining model. From this study, it was found that the contour map by Wavelet transform provides more distinct results than the power spectrum by Fourier transform and it was concluded that Wavelet transform was an effective tool for the experimental analysis of dispersive waves in concrete structures.

• Economic and Environmental Geology
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• v.28 no.5
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• pp.527-533
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• 1995

A disadvantage of Fourier analysis is that frequency information can only be extracted for the complete duration of a signal f(t). Since the Fourier transform integral extends over all time, from $-{\infty}$ to $+{\infty}$), the information it provides arises from an average over the whole length of the signal. If there is a local oscillation representing a particular feature, this will contribute to the calculated Fourier transform $F({\omega})$, but its location on the time axis will be lost There is no way of knowing whether the value of $F({\omega})$ at a particular ${\omega}$ derives from frequencies present throughout the life of f(t) or during just one or a few selected periods. This disadvantage is overcome in wavelet analysis which provides an alternative way of breaking a signal down into its constituent parts. The main advantage of the wavelet transform over the conventional Fourier transform is that it can not only provide the combined temporal and spectral features of the signal, but can also localize the target information in the time-frequency domain simultaneously. The wavelet transform distinguishes itself from Short Time Fourier Transform for time-frequency analysis in that it has a zoom-in and zoom-out capability.

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.541-555
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• 1996

The Fourier transform plays a central role in the theory of distribution on Euclidean spaces. Although Lebesgue measure does not exist in infinite dimensional spaces, the Fourier transform can be introduced in the space $(S)^*$ of generalized white noise functionals. This has been done in the series of paper by H.-H. Kuo [1, 2, 3], [4] and [5]. The Fourier transform $F$ has many properties similar to the finite dimensional case; e.g., the Fourier transform carries coordinate differentiation into multiplication and vice versa. It plays an essential role in the theory of differential equations in infinite dimensional spaces.

• Korean Journal of Mathematics
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• v.12 no.2
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• pp.193-200
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• 2004

We shall introduce the notion of the windowed Fourier transform in $\mathbb{Q}_p$ and show that, for any given function $g{\in}L^2(\mathbb{Q}_p)$ of norm, the windowed Fourier transform of $f$ with respect to $g$ be a function of norms, and moreover be expressible to a summation form. The results obtained in this paper will be usable to the field of research in data compression for signal processing according to the following scheme.

• Journal of Korean Academy of Oral and Maxillofacial Radiology
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• v.28 no.2
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• pp.339-353
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• 1998

The purpose of this study was to investigate whether a radiographic estimate of osseous fractal dimension and power spectrum of 2D discrete Fourier transform is useful in the characterization of structural changes in bone. Ten specimens of bone were decalcified in fresh 50 ml solutions of 0.1 N hydrochloric acid solution at cummulative timed periods of 0 and 90 minutes. and radiographed from 0 degree projection angle controlled by intraoral parelleling device. I performed one-dimensional variance. fractal analysis of bony profiles and 2D discrete Fourier transform. The results of this study indicate that variance and fractal dimension of scan line pixel intensities decreased significantly in decalcified groups but Fourier spectral analysis didn't discriminate well between control and decalcified specimens.

• Journal of Korea Water Resources Association
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• v.38 no.6 s.155
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• pp.439-448
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• 2005

This paper introduces the wavelet transform that was improved by the fourier transform to assess periodicities and trends, we assessed propriety with examples of two monthly precipitation data, annual precipitation, SOI index and SST index. The wavelet transform can effectively assess the power spectrum corresponding to frequency as maintaining chronological characteristics. The results of the analysis using the wavelet transform showed that the monthly precipitation have the strongest power spectrum near that of 1 year, and the annual precipitation represent the dominated spectrum in the band of 2-8 years. Also, the SOI index and SST index indicate the strongest power spectrum in the band of 2-8 years.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.21 no.3
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• pp.75-81
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• 2007

Recently the subject of "wavelet analysis" has be drawn by both mathematical and engineering application fields such as Signal Processing, Compression/Decomposition, Wavelet-Neural Network, Statistics and etc. Even though its similar to Fourier analysis, wavelet is a versatile tool with much mathematical content and great potential for applications. Especially, wavelet transform uses localizable various mother wavelet functions in time-frequency domain. Therefore, wavelet transform has good time-analysis ability for high frequency component, and has good frequency-analysis ability for low frequency component. Using the discriminative ability is more easy method than other conventional techniques. In this paper, Morlet wavelet transform was applied to discriminate the kind of line fault by acquired data from real power transformation network. The experimental result presented that Morlet wavelet transform is easier, and more useful method than the Fast Fourier Transform(FFT).