• Journal of the Korean Data and Information Science Society
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• 제15권2호
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• pp.467-476
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• 2004

Recently, an approximation of a wavelet series has been developed in the analyses of an unknown function. Most of articles have been studied on thresholding and shrinkage methods for its wavelet coefficients based on (non)parametric and Bayesian methods when the sample size is considered as a maximum resolution in wavelet series. In this paper, regardless of the sample size, we are focusing only on the choice of a maximum resolution in wavelet series. We propose a Bayesian approach to the choice of a maximum resolution based on the linear combination of the wavelet basis functions.

• 한국해양공학회:학술대회논문집
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• 한국해양공학회 2000년도 추계학술대회 논문집
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• pp.118-122
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• 2000

In this study, Ringing is investigated by continuous wavelet transform. Ringing is considered to be one of the typical transient phenomena in the field of ocean engineering. The wavelet analysis is adopted to analyze ringing from the point that wavelet analysis is capable of frequency analysis as well as time domain analysis. The use mother wavelet is the Morlet wavelet. The relation between the frequency of the time series and that of wavelet can be clearly defined with Mor1et wavelet. Experimental data obtained by other researchers was used. The wave height time series and acceleration times series of the surface piercing cylinder were analyzed. The results show that the proposed scheme can detect typical frequency region by the time domain analysis which could hardly be detected if one relied on the frequency analysis.

• 전기학회논문지
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• 제57권3호
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• pp.494-500
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• 2008

This paper presents the analyzed result of the series arc fault current by using the discrete wavelet transform. The series arcing is caused by a loose connection in series with the load circuit. The series arc current is limited to a moderate value by the resistance of the device connected to the circuit, such as an appliance or a lighting system. The amount of energy in the sparks from the series arcing is less than in the case of parallel arcing but only a few amps are enough to be a fire hazard. Therefore, it is hard to detect the distinctive difference between a normal current and a intermittent arc current. This paper, presents the variation of the ratio of peak values and RMS values of the series arc fault current, and proposes the novel series arc fault detecting method by using the discrete wavelet transform. Loads such as a CFL lamp, a vacuum cleaner, a personal computer, and a television, which has the very similar normal current with the arc current, were selected to confirm the novel method.

• 대한수학회논문집
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• 제13권1호
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• pp.181-193
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• 1998

The Shannon sampling series is the prototype of an interpolating series or sampling series. Also the Shannon wavelet is one of the protypes of wavelets. But the coefficients of the Shannon sampling series are different function values at the point of discontinuity, we analyze the Gibbs phenomenon for the Shannon sampling series. We also find a way to go around this overshoot effect.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2007년도 학술발표회 논문집
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• pp.1437-1440
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• 2007

Many hydroclimatic time series are marked by interannual and longer quasi-period features that are associated with narrow band oscillatory climate modes. A time series modeling approach that directly considers such structures is developed and presented. The essence of the approach is to first develop a wavelet decomposition of the time series that retains only the statistically significant wavelet components, and to then model each such component and the residual time series as univariate autoregressive processes. The efficacy of this approach is demonstrated through the simulation of observed and paleo reconstructions of climate indices related to ENSO and AMO, tree ring and rainfall time series. Long ensemble simulations that preserve the spectral attributes of the time series in each ensemble member can be generated. The usual low order statistics are preserved by the proposed model, and its long memory performance is superior to the direction application of an autoregressive model.

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.419-426
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• 2009

In expansion of function by special basis functions, properties of expansion kernel are very important. In the Fourier series, the series are expressed by the convolution with Dirichlet kernel. We investigate some of properties of kernel in wavelet expansions both in one and higher dimensions.

• 한국데이터정보과학회:학술대회논문집
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• 한국데이터정보과학회 2005년도 춘계학술대회
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• pp.83-126
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• 2005

Single-index models have found applications in econometrics and biometrics, where multidimensional regression models are often encountered. Here we propose a nonparametric estimation approach that combines wavelet methods for non-equispaced designs with Bayesian models. We consider a wavelet series expansion of the unknown regression function and set prior distributions for the wavelet coefficients and the other model parameters. To ensure model identifiability, the direction parameter is represented via its polar coordinates. We employ ad hoc hierarchical mixture priors that perform shrinkage on wavelet coefficients and use Markov chain Monte Carlo methods for a posteriori inference. We investigate an independence-type Metropolis-Hastings algorithm to produce samples for the direction parameter. Our method leads to simultaneous estimates of the link function and of the index parameters. We present results on both simulated and real data, where we look at comparisons with other methods.

• Journal of applied mathematics & informatics
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• 제9권2호
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• pp.657-666
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• 2002

ThE Gibbs' phenomenon in the classical Fourier series is well-known. It is closely related with the kernel of the partial sum of the series. In fact, the Dirichlet kernel of the courier series is not positive. The poisson kernel of Cesaro summability is positive. As the consequence of the positiveness, the partial sum of Cesaro summability does not exhibit the Gibbs' phenomenon. Most kernels associated with wavelet expansions are not positive. So wavelet series is not free from the Gibbs' phenomenon. Because of the excessive oscillation of wavelets, we can not follow the techniques of the courier series to get rid of the unwanted quirk. Here we make a positive kernel For Meyer wavelets and as the result the associated summability method does not exhibit Gibbs' phenomenon for the corresponding series .

• East Asian mathematical journal
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• 제26권1호
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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.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1999년도 하계학술대회 논문집 B
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• pp.969-971
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• 1999

Wavelet analysis is applying to many fields such as the time-frequency localization of a time series and a time varying data. In this paper, a statistical testing based Wavelet power spectrum analysis for the stationary Nino3 Sea Surface Temperature(SST) data was executed. Specially, the 95% confidence level for SST was effective in searching the periods of El-Nino using various wavelet basis functions.