• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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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.

• Korean Journal of Optics and Photonics
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• v.14 no.3
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• pp.266-271
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• 2003

The reflectance spectrum of optical films thicker than a few microns shows an intensity oscillation due to interference. Since the spectral period of the oscillation is inversely related to film thickness, the thickness of an optical film can be determined from the spectral frequency of the oscillation. For rapid data processing, the spectral frequency is obtained by use of a Fast Fourier Transformation technique. The conventional method of applying a Fast Fourier Transformation to the reflectance spectrum versus photon energy is modified so as to clear the ambiguity in choosing the proper effective refractive index value and to prevent the broadening of the Fourier transformed peak due to the refractive index dispersion. This technique of modified Fast Fourier Transformation is suggested by the authors for the first time to their knowledge. From the analysis of the calculated reflectance spectrum of a 30-${\mu}{\textrm}{m}$-thick dielectric film. it is shown to improve the accuracy in determining film thickness by a great amount. The improved accuracy of the modified Fast Fourier Transformation is also confirmed from the analysis of the reflectance spectra of a sample with 80-${\mu}{\textrm}{m}$-thick cover layer and 13-${\mu}{\textrm}{m}$-thick spacer layer on a PC substrate.

• 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 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.

• Journal of the Korean Society of Safety
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• v.20 no.3 s.71
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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.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.6
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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.

• Korean Journal of Optics and Photonics
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• v.6 no.3
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• pp.245-256
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• 1995

Rugate filters of inhomogeneous refractive index were designed using the Fourier transform and the effect of reflectance, stop bandwidth, optical thickness, and Q function on the rugate filter was investigated. An iterative correction process using a merit function was employed to fit an initial design to the target spectrum. Three Q functions derived by Sossi, Bovard, and Fabricius, respectively, were compared in terms of the number of iteration, merit function, and optimum optical thickness. The result shows that after a number of iterations the Q functions by Bovard and Fabricius produce high rejection rugate filters closer to the target spectrum than the Sossi's Q function and the optimal optical thickness is determined by the stop-band width of the rugate filter. ilter.

• Journal of the Ergonomics Society of Korea
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• v.31 no.2
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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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• v.35 no.4
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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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• v.27 no.5
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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.