• 대한수학회보
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• 제57권2호
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• pp.481-488
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• 2020

In this paper we give an exact formula for the Fourier coefficients of the Jacobi-Eisenstein series of square free discriminant lattice index. For a special case the discriminant of lattice is prime we show that the Jacobi-Eisenstein series corresponds to a well known Eisenstein series of modular forms.

• 한국광학회지
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• 제14권3호
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• pp.266-271
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• 2003

수 $\mu\textrm{m}$ 이상의 두께를 가지는 비교적 두꺼운 박막의 경우 박막에 의한 간섭효과로 인하여 나타나는 반사율 스펙트럼에서의 진동주기로부터 막의 두께를 얻는다. 대개 빠른 데이터 처리를 위해서 고속 푸리에 변환(Fast Fourier Transformation, FFI)을 사용하여 진동주기(또는 진동수)를 구한다. 본 연구에서는 반사율 또는 투과율 스펙트럼을 빛의 에너지 축상에서 푸리에 변환하는 종래의 방법을 개선하여 박막의 굴절률 분산을 반영하는 수정된 고속 푸리에 변환 방법을 최초로 도입하였다. 이 새로운 방법은 굴절률 분산에서 유래하는 유효굴절률 결정에서의 오차를 줄여주고 푸리에 변환 피크의 폭 넓어짐을 막아줌으로써 막 두께 결정의 정밀도를 크게 향상시킨다. 수정된 고속 푸리에 변환방법을 80 $\mu\textrm{m}$의 덮게층과 13 $\mu\textrm{m}$의 사이층이 있는 시료의 반사 스펙트럼에 적용하여 고 타당성을 확인하였다.

• 한국수자원학회논문집
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• 제38권6호
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• pp.439-448
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• 2005

본 논문은 수문시계열에서 나타나는 주기성 및 경향성 등을 평가하기 위한 방법으로 Fourier Transform을 개선한 Wavelet Transform방법을 제시하고 이에 대한 타당성 및 적용성을 월강수량 및 연강수량 자료와 대표적인 기상인자인 남방진동지수(SOI)와 해수면온도(SST)를 대상으로 평가해 보았다. Fourier Transform은 시간적인 특성을 파악하지 못하는 반면에 Wavelet Transform은 수문시계열이 갖는 시간적인 특성을 유지하면서 빈도에 대한 스펙트럼을 보다 효율적으로 평가할 수 있었다. Wavelet Transform을 이용하여 분석한 결과 국내 월강수량은 1년을 중심으로 강한 스펙트럼을 나타내고 있으며 연강수량은 2-8년 주기에서 통계적으로 유의한 주기를 확인할 수 있었다. SOI와 SST에서는 2-8년 주기가 지배적임을 확인할 수 있었다.

• 한국진공학회지
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• 제16권6호
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• pp.458-462
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• 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.

• 한국안전학회지
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• 제20권3호
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• pp.64-70
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• 2005

In this literature, fault detection and classification of faulty induction motors are carried out through Z-index and frequency analysis. Above frequency analysis refer Fourier transformation and Wavelet transformation. Z-index is defined as the similar form of energy function, also the faulty and healthy conditions are classified through Z-index. For the detection and classification feature extraction for the fault detection of an induction motor is carried out using the information from stator current. Fourier and Wavelet transforms are applied to detect the characteristics under the healthy and various faulty conditions. We can obtain feature vectors from two transformations, and the results illustrate that the feature vectors are complementary each other.

• 전기학회논문지
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• 제58권6호
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• pp.1078-1086
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• 2009

This paper presents a Fourier based algorithm for estimating the parameters of the low frequency oscillating modes. The proposed methods estimates various parameters(frequency, damping factor, mode magnitude, phase) by fitting Fourier spectrum and phase with a damped exponential cosine function. Dominant frequency is selected by taking frequency corresponding to the peak spectrum, and damping factor is estimated using the left/right spectra of Fourier spectrum. In addition, mode magnitude is calculated by the normalized peak spectrum, and phase is estimated from spectrum phase. Also, we introduce an accuracy index in order to determine the accuracy of the estimated parameters, and the index is calculated using the deviations of the peak spectrum and the left/right spectra. The parameter estimation methods proposed in this paper include very simple arithmetical processes, so the algorithms are simple and the calculation speed is very fast. The proposed methods are applied to test functions with two dominant modes. The results show that the proposed methods are highly applicable to low frequency parameter estimation.

• 한국광학회지
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• 제6권3호
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• pp.245-256
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• 1995

Fourier 면환을 이용하여 불균일 굴절률 박막의 rugate 필터를 설계하였으며 rugate 필터의 반사율, 대역폭, 광학 두께, Q 함수 등을 변화시키며 Fourier 변환의 여러 가지 특성을 조사하였다. 주어진 단선 및 이중 rugate 필터의 과녁 스펙트럼에 불균일 굴절률 박막의 스펙트럼을 맞추기 위하여 merit 함수를 사용하였으며 merit 값이 최소가 되도록 Q 함수를 반복계산하여 수정하였다. Sossi, Bovard, Fabricius가 각각 유도한 세 종류의 Q함수를 반복계산 횟수, merit 함수의 값, 최적 광학두께 등의 관점에서 비교하였다. 반사율이 높은 rugate 필터 설계에는 반복계산 수정 후 반사율이 과녁스펙트럼에 가까운 Bovard와 Fabricius의 Q함수가 적당하며, 광학 두께는 최소 광학두께만 넘으면 반복계산 수정과정을 이용하여 과녁반사율을 맞출 수 있으므로 반사대역폭이 허용하는 광학두께로 결정하면 될 것이다.

• 대한인간공학회지
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• 제31권2호
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• pp.337-343
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• 2012

Objective: The aim of this study was to determine the effect of abdominal-compression belt in one leg standing on balance in normal adult. Background: With the effects of increased intra-abdominal pressure, the abdominal-compression belt is contributing to a static balance control. However, specific study is still insufficient. Method: Forty subjects were randomly allocated to two groups: control(n=20) and experimental group(n=20), respectively. The experimental group used an abdominal-compression belt, whereas the control group did not that. All subjects were educated using pressure biofeedback unit and ultrasound imaging for exact application by abdominal-compression belt. Main outcome measurement was used a general stability index, fourier harmony index, weight distribution index, and fall index in tetrax balance system. Results: Experimental group improved significantly on general stability, only 2 factors(eyes closed with head turned forward and eyes closed with head turned backward) among fourier harmony index, and fall index, However, weight distribution index did not revealed significant difference. Conclusion: The findings suggest that application of abdominal-compression belt could be effective on improving balance ability in one leg standing of normal adults. Application: The results of the abdominal-compression belt might help to control balance in workers.

• The Journal of Korean Physical Therapy
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• 제35권4호
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• pp.105-110
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• 2023

Purpose: The purpose of this study was to determine whether the degree of dizziness affects static balance due to the disruption or absence of the senses involved in balance. To this end, the correlation between the Dizziness Handicap Inventory (DHI), which objectively evaluates dizziness, the Fourier Index (FI; Frequency bands of postural oscillation, F1, F2-4, F5-6, F7-8) and the Stability Index (ST), which evaluates static balance ability, were examined. Methods: This study investigated balance and dizziness issues in 30 healthy young adults. Participants underwent multiple tests like the DHI and tetra-ataxiometric posturography (Tetrax) under different conditions (eyes open/closed, standing on a foam-rubber pillow, and with the head in various orientations). Results: We found that F1 exhibited a weak positive correlation with dizziness under normal conditions, as well as when the eyes were closed (r=0.396, p<0.05) and the head was tilted back (r=0.375, p<0.05). Meanwhile, F5-6 showed a moderate positive correlation with dizziness in both head-back (HB: r=0.471, p<0.05) and head-forward postures (r=0.404, p<0.05). Lastly, both F7-8 and ST demonstrated a moderate positive correlation with dizziness when the head was in a forward posture (F7-8: r=0.483; ST: r=0.403, p<0.05). Conclusion: The study results indicate that the severity of dizziness affects sensory systems and balance. It also suggests that head movements, especially forward and backward, further stimulate the vestibular system, intensifying dizziness, and balance problems in affected individuals.

• Computers and Concrete
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• 제27권5호
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• pp.447-455
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• 2021

Research on damage detection methods in structures began a few decades ago with the introduction of methods based on structural vibration frequencies, which, of course, continues to this day. The value of important structures, on the one hand, and the countless maintenance costs on the other hand, have led researchers to always try to identify more accurate methods to diagnose damage to structures in the early stages. Among these, one of the most important and widely used methods in damage detection is the use of time-frequency representations. By using time-frequency representations, it is possible to process signals simultaneously in the time and frequency domains. In this research, the Short-Time Fourier transform, a known time-frequency function, has been used to process signals and identify the system. Besides, a new damage index has been introduced to identify damages in concrete piers of bridges. The proposed method has relatively simple calculations. To evaluate the method, the finite element model of an existing concrete bridge was created using as-built details. Based on the results, the method identifies the damages with high accuracy.