• East Asian mathematical journal
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• v.26 no.1
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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.

• Communications for Statistical Applications and Methods
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• v.10 no.3
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• pp.955-969
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• 2003

The classical Fourier analysis, which is the typical frequency domain approach, is used to detect periodic trends that are of the sinusoidal shape in time series data. In this article, using a sequence of periodic step functions, describes an adaptive Fourier series where the patterns may take general periodic shapes that include sinusoidal as a special case. The results, which extend both Fourier analysis and Walsh-Fourier analysis, are applies to investigate the shape of the periodic component. Through the real data, compare the goodness-of-fit of the model using two methods, the adaptive Fourier method which is proposed method in this paper and classical Fourier method.

• 제어로봇시스템학회:학술대회논문집
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• 1986.10a
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• pp.61-64
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• 1986

The Fourier Spectral Analysis has been widely utilized in the analysis of linear dynamic systems. However, it may not be generaly extended to analyze nonlinear systems. In this paper, a linear underlying dynamic structure coupled with nonlinear elements is analyzed by using newly derived equations of motion after the linear dynamic structure is characterized by the Fourier spectral analysis.

• 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.

• 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.

• The Journal of Korean Medicine
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• v.32 no.4
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• pp.139-148
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• 2011

Objective: The purpose of this study was to investigate the effect of food intake on the Fourier components of radial pulse wave. Methods: Thirty-one healthy male subjects participated in this study. Radial pulse was measured using 3 dimensional pulse imaging system (DMP-3000) before, right after, 40 minutes after, 80 minutes after and 120 minutes after food intake. Fourier transform was performed and the frequency and amplitude of Fourier components were analyzed. Results: 1. The frequency and the amplitude of Fourier components of radial pulse wave increased significantly after food intake. 2. The frequency of Fourier components increased right after food intake and then gradually decreased as time passed, however the amplitude of Fourier components increased and maintained certain levels and patterns throughout the experimental period of 120 minutes. 3. The change ratios of the frequency and the amplitude of Fourier components after food intake varied with the pulse measuring locations. Conclusions: Food intake exerts an influence on radial pulse wave, resulting in increase of frequency and amplitude of Fourier components. The change ratios of the frequency and the amplitude of Fourier components after food intake varied with the pulse measuring locations.

• IEIE Transactions on Smart Processing and Computing
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• v.4 no.2
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• pp.103-109
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• 2015

In this paper, a novel method for the classification of term and preterm birth is proposed based on time-frequency analysis of electrohysterogram (EHG) using multivariate empirical mode decomposition (MEMD). EHG is a promising study for preterm birth prediction, because it is low-cost and accurate compared to other preterm birth prediction methods, such as tocodynamometry (TOCO). Previous studies on preterm birth prediction applied prefilterings based on Fourier analysis of an EHG, followed by feature extraction and classification, even though Fourier analysis is suboptimal to biomedical signals, such as EHG, because of its nonlinearity and nonstationarity. Therefore, the proposed method applies prefiltering based on MEMD instead of Fourier-based prefilters before extracting the sample entropy feature and classifying the term and preterm birth groups. For the evaluation, the Physionet term-preterm EHG database was used where the proposed method and Fourier prefiltering-based method were adopted for comparative study. The result showed that the area under curve (AUC) of the receiver operating characteristic (ROC) was increased by 0.0351 when MEMD was used instead of the Fourier-based prefilter.

• Journal of the Korean Vacuum Society
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• v.16 no.6
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• pp.458-462
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• 2007

Spectroscopic ellipsometry is an excellent technique for determining dielectric function. To obtain critical point energy, standard analytic critical point expression is used conventionally for second derivatives of dielectric function which might increase high frequency noise than signal. However, reciprocal-space analysis offers several advantages for determining critical point parameters in optical and other spectra, for example the separation of baseline, information, and high frequency noise in low-, medium-, high-index Fourier coefficient, respectively. We used reciprocal Fourier analysis for removing noise and determining critical point of ZnCdSe alloy.

• KOREAN JOURNAL OF CROP SCIENCE
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• v.50 no.1
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• pp.60-66
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• 2005

Pod shape of twenty soybean (Glycine max L. Merrill) genotypes was evaluated quantitatively by image analysis using elliptic Fourier descriptors and their principal components. The closed contour of each pod projection was extracted, and 80 elliptic Fourier coefficients were calculated for each contour. The Fourier coefficients were standardized so that they were invariant of size, rotation, shift, and chain code starting point. Then, the principal components on the standardized Fourier coefficients were evaluated. The cumulative contribution at the fifth principal component was higher than $95\%$, indicating that the first, second, third, fourth, and fifth principal components represented the aspect ratio of the pod, the location of the pod centroid, the sharpness of the two pod tips and the roundness of the base in the pod contour, respectively. Analysis of variance revealed significant genotypic differences in these principal components and seed number per pod. As the principal components for pod shape varied continuously, pod shape might be controlled by polygenes. It was concluded that principal component scores based on elliptic Fourier descriptors yield seemed to be useful in quantitative parameters not only for evaluating soybean pod shape in a soybean breeding program but also for describing pod shape for evaluating soybean germplasm.

• 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.