• East Asian mathematical journal
• /
• 제26권1호
• /
• pp.105-113
• /
• 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
• /
• 제10권3호
• /
• pp.955-969
• /
• 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
• /
• 제어로봇시스템학회 1986년도 한국자동제어학술회의논문집; 한국과학기술대학, 충남; 17-18 Oct. 1986
• /
• pp.61-64
• /
• 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.

• 한국전자파학회논문지
• /
• 제19권9호
• /
• pp.968-977
• /
• 2008

본 논문에서는 Fourier-transform analysis와 Wiener-Hopf technique을 사용하여 병렬 슬릿에 의한 TE파 산란의 완전한 표현식을 유도하고 두 방법의 특징을 비교하고자 한다. Fourier transform analysis는 슬릿의 폭이 좁은 경우에는 빠른 수렴해를 얻을 수 있으며, Wiener-Hopf technique은 슬릿의 폭이 넓을 경우(상호 유도 결합이 적은 경우)에 매우 정확한 근사식 결과를 나타내며, 위의 두 해석 결과는 비교적 일치하는 결과들을 보여준다.

• Journal of applied mathematics & informatics
• /
• 제26권5_6호
• /
• pp.1101-1121
• /
• 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.

• 대한한의학회지
• /
• 제32권4호
• /
• pp.139-148
• /
• 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
• /
• 제4권2호
• /
• pp.103-109
• /
• 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.

• 한국진공학회지
• /
• 제16권6호
• /
• pp.458-462
• /
• 2007

타원편광분석법은 반도체 물질의 광 특성과 전이점 연구에 유용하게 쓰이는 기술이다. 측정된 유전율 함수로부터 전이점을 구하기 위해서 전통적으로 이차 미분스펙트럼을 이용하여 분석하는데, 이 방법은 high frequency 의 잡음을 크게 증폭시키는 단점이 있다. 본 연구에서는 역 공간 푸리에 변환 (Fourier transform)을 이용하여 low-, medium-, high-index 의 푸리에 계수로부터 baseline, 정보, high frequency 잡음을 분리하는 방법을 소개하고자 한다. 이 방법을 이용하여 광전자소자에 폭넓게 사용되는 ZnCdSe 화합물 반도체의 $E_1,\;E_1+{\Delta}_1$ 전이점에 대한 연구를 하여 전통적인 이차 미분법과 비교해 보았다.

• 한국작물학회지
• /
• 제50권1호
• /
• pp.60-66
• /
• 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
• /
• 제26권1호
• /
• pp.105-115
• /
• 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.