• Journal of Korea Water Resources Association
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• v.52 no.11
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• pp.905-916
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• 2019

This study explores the effect of mother wavelet in the bivariate wavelet analysis. A total of four mother wavelets (Bump, Mexican hat, Morlet, and Paul) which are frequently used in the related studies is selected. These mother wavelets are applied to several bivariate time series like white noise and sine curves with different periods, whose results are then compared and evaluated. Additionally, two real time series such as the arctic oscillation index (AOI) and the southern oscillation index (SOI) are analyzed to check if the results in the analysis of generated time series are consistent with those in the analysis of real time series. The results are summarized as follows. First, the Bump and Morlet mother wavelets are found to provide well-matched results with the theoretical predictions. On the other hand, the Mexican hat and Paul mother wavelets show rather short-periodic and long-periodic fluctuations, respectively. Second, the Mexican hat and Paul mother wavelets show rather high scale intervention, but rather small in the application of the Bump and Morlet mother wavelets. The so-called co-movement can be well detected in the application of Morlet and Paul mother wavelets. Especially, the Morlet mother wavelet clearly shows this characteristic. Based on these findings, it can be concluded that the Morlet mother wavelet can be a soft option in the bivariate wavelet analysis. Finally, the bivariate wavelet analysis of AOI and SOI data shows that their periodic components of about 2-4 years co-move regularly every about 20 years.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.8
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• pp.1470-1477
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• 2008

In this paper, a new detection method of series arc-fault signals occurring at the wiring of home appliances is proposed. The discrete wavelet transform was used for the numerical analysis of the variation rate in peak, RMS, noise energy, shoulder of the arc-fault current wave. As a results, the arc distinction threshold value of these variation rates was about 0.1 in most cases. The arc-fault current of the loads with the active PFC circuit showed a high rate of variation in noise energy and shoulder, but arc-fault current of the loads without the active PFC circuit showed a high rate of variation in peak and RMS. The arc fault current in resistive loads showed a high rate of variation in shoulder.

• Journal of Korea Water Resources Association
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• v.52 no.8
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• pp.575-587
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• 2019

This study evaluated the effect of a mother wavelet in the wavelet analysis of various times series made by combining white noise and/or sine function. The result derived is also applied to short-memory arctic oscillation index (AOI) and long-memory southern oscillation index (SOI). This study, different from previous studies evaluating one or two mother wavelets, considers a total of four generally-used mother wavelets, Bump, Morlet, Paul, and Mexican Hat. Summarizing the results is as follows. First, the Bump mother wavelet is found to have some limitations to represent the unstationary behavior of the periodic components. Its application results are more or less the same as the spectrum analysis. On the other hand, the Morlet and Paul mother wavelets are found to represent the non-stationary behavior of the periodic components. Finally, the Mexican Hat mother wavelet is found to be too complicated to interpret. Additionally, it is also found that the application result of Paul mother wavelet can be inconsistent for some specific time series. As a result, the Morlet mother wavelet seems to be the most stable one for general applications, which is also assured by the recent trend that the Morlet mother wavelet is most frequently used in the wavelet analysis research.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.09a
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• pp.322-325
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• 2003

In this paper, we propose n new fuzzy model identification of time series system using wavelet transform and genetic DNA code. Generally, it is well known that the DNA coding method is more diverse in the knowledge expression and better in the optimization performance than the genetic algorithm (GA) because it can encode more plentiful genetic information based on the biological DNA. The proposed method can construct a fuzzy model using the wavelet transform, in which the coefficients are identified by the DNA coding method. Thus, we can effectively get the fuzzy model of the nonlinear system by using the advantages of both wavelet transform and DNA coding method. In order to demonstrate the superiority of the proposed method, it is compared with modeling method using the conventional GA.

• Journal of Institute of Control, Robotics and Systems
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• v.7 no.5
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• pp.415-419
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• 2001

This paper proposes and adaptive nonlinear equalizer based on Volterra Series along with M-band wavelet transform(M-DWT). The proposed wavelet transform-domain approach leads to diagonalization of the input vector auto-correlation matrix, which yields clustering its eigenvalue spread around one, and improving the convergence rate of the corresponding transform-domain LMS algorithm. In particular, the proposed adaptive Volterra equalizer is employed to compensate for the output distortion produced by a weakly nonlinear system. Finally, some simulation results obtained by using a TWT amplifier model are provide to demonstrated the converging performance of the proposed approach.

• The Korean Journal of Applied Statistics
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• v.23 no.2
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• pp.249-261
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• 2010

Long-term forecasting of seasonal time series is critical in many applications such as planning business strategies and resolving possible problems of a business company. Unlike the traditional approach that depends solely on dynamic models, Li and Hinich (2002) introduced a combination of stochastic dynamic modeling with filter bank approach for forecasting seasonal patterns using highly coherent(High-C) waveforms. We modify the filter selection and forecasting procedure on wavelet domain to be more feasible and compare the resulting predictor with one that obtained from the wavelet variance estimation method. An improvement over other seasonal pattern extraction and forecasting methods based on such as wavelet scalogram, Holt-Winters, and seasonal autoregressive integrated moving average(SARIMA) is shown in terms of the prediction error. The performance of the proposed method is illustrated by a simulation study and an application to the real stock price data.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2003.05a
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• pp.324-329
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• 2003

Spectral analysis is an important signal processing tool for time series data. The transformation of a time series into the frequency domain is the basis for a significant number of processing algorithms and interpretive methods. Recently developed transforms based on the new mathematical field of wavelet analysis bypass the resolution limitation and offer superior spectral decomposition. The discrete wavelet transform of Sonar data provides spectral localization of noises, hence noises can be filtered out successfully.

• Journal of Korea Multimedia Society
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• v.3 no.5
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• pp.461-469
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• 2000

A wavelet analysis in a field of analytics is to create a reconstruction theorem of Plancherel form. And a series of wavelet is to create a discrete is to create a discrete reconstruction theorem for a frame theory and a multiresolution analysis theory. As a generation of reconstruction theorem, a wavelet correspond to it is generated. That is to be like a basic wavelet which is satisfied an admissibility condition in CWT and a Daubechies wavelet using MRA in wavelet series and a Meyer wavelet using a frame theory. In this paper, we discover a discrete reconstruction theorem which is superior to a conventional discrete reconstruction theorem by extending admissibility condition used in CWT and develop a New $L^1$-wavelet group. A new $L^1$-wavelet is applied to a signal reconstruction and a signal analysis in time-frequency region.

• Proceedings of the IEEK Conference
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• 2005.11a
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• pp.343-346
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• 2005

In this study, a basic concept of wavelet encoding and its advantages over Fourier based phase encoding application. Wavelet encoding has been proposed as an alternative way to Fourier based phase encoding in magnetic resonance imaging. In wavelet encoding, the RF pulse is designed to generate wavelet-shaped excitation profile of spins. From the resulting echo signals, the wavelet transform coefficients of spin distribution are acquired and an original spin density is reconstructed from wavelet expansion. Wavelet encoding has several advantages over phase encoding. By minimizing redundancy of the data acquisition in a dynamic series of images, we can avoid some encoding steps without serious loss of quality in reconstructed image. This strategy may be regarded as data compression during imaging. Although there are some limitations in wavelet encoding, it is a promising scheme in a dynamic imaging.

• International Journal of Ocean Engineering and Technology Speciallssue:Selected Papers
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• v.6 no.1
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• pp.1-6
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• 2003

This study presents the results of series of studies, which are mainly devoted to the application of wavelet transforms to various problems in ocean engineering. Both continuous and discrete wavelet transforms were used. These studies attempted to solve detection of wave directionality, detection of wave profile, and decoupling of the rolling component from free roll decay tests. The results of these analysis, using wavelet transform, demonstrated that the wavelet transform can be a useful tool in analyzing many problems in the filed of ocean engineering.