• Communications of the Korean Mathematical Society
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• v.15 no.2
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• pp.285-308
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• 2000

We generalize bi-orthogonal (non-orthogona) MRA to frame MRA in which the family of integer translates of a scaling func-tion forms a frame for the initial ladder space V0. We investigate the internal structure of frame MRA and establish the existence of a dual scaling function, and show that, unlike bi-orthogonal MRA, there ex-ists a frame MRA that has no (frame) 'wavelet'. Then we prove the existence of a dual wavelet under the assumption of the existence of a wavelet and present easy sufficient conditions for the existence of a wavelet. Finally we give a new proof of an equivalent condition for the translates of a function in L2(R) to be a frame of its closed linear span.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.23 no.1
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• pp.1-8
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• 2010

The Fourier series uses a vibrating wave that possesses an amplitude that is like the one of the sine curve. Therefore, the functions used in the Fourier series do not change due to the value of the frequency and that set a limit to express irregular signals with rapid oscillations or with discontinuities in localized regions. However, the wavelet series analysis(WSA) method supplements these limits of the Fourier series by a linear combination of a suitable number of wavelets. By using the wavelet that is focused on time, it is able to give changes to the range in the cycle. Also, this enables to express a signal more efficiently that has singular configuration and that is flowing. The main objective of this study is to propose a scheme called wavelet series analysis for the application of wavelet theory to one-dimensional problems represented by the second-order elliptic equation and to evaluate theperformance of proposed scheme comparing with the finite element analysis. After a through evaluation of different types of wavelets, the HAT wavelet system is chosen as a wavelet function as well as a scaling function. It can be stated that the WSA method is as efficient as the FEA method in the case of axial bars with distributed loads, but the WSA method is more accurate than the FEA method at the singular points and its computation time is less.

• Journal of the Korean Society for Precision Engineering
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• v.19 no.12
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• pp.78-85
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• 2002

The wavelet transform is a popular tool fer studying intermittent and localized phenomena in signals. In this study the wavelet transform of cutting force signals was conducted for the detection of a tool failure in turning process. We used the Daubechies wavelet analyzing function to detect a sudden change in cutting signal level. A preliminary stepped workpiece which had intentionally a hard condition was cut by the inserted cermet tool and a tool dynamometer obtained cutting force signals. From the results of the wavelet transform, the obtained signals were divided into approximation terms and detailed terms. At tool failure, the approximation signals were suddenly increased and the detailed signals were extremely oscillated just before tool failure.

• The Journal of the Acoustical Society of Korea
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• v.27 no.3E
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• pp.77-83
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• 2008

In the process of the sonar image textures produced, the orientation and scale factors are very significant. However, most of the related methods ignore the directional information and scale invariance or just pay attention to one of them. To overcome this problem, we apply Gabor wavelet to extract the features of sonar images, which combine the advantages of both the Gabor filter and traditional wavelet function. The mother wavelet is designed with constrained parameters and the optimal parameters will be selected at each orientation, with the help of bandwidth parameters based on the Fisher criterion. The Gabor wavelet can have the properties of both multi-scale and multi-orientation. Based on our experiment, this method is more appropriate than traditional wavelet or single Gabor filter as it provides the better discrimination of the textures and improves the recognition rate effectively. Meanwhile, comparing with other fusion methods, it can reduce the complexity and improve the calculation efficiency.

• Journal of the Korean Magnetic Resonance Society
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• v.4 no.2
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• pp.103-115
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• 2000

Wavelet transforms are introduced as a new tool to distinguish real peaks from the noise contaminated NMR data in this paper. New algorithms of two wavelet transforms including Daubechies wavelet transform as a discrete and orthogonal wavelet transform (DWT) and Morlet wavelet transform as a continuous and nonorthogonal wavelet transform(CWT) were developed fer noise elimination. DWT and CWT method were successfully applied to the noise reduction in spectrum. The inevitable distortion of NMR spectral baseline and the imperfection in noise elimination were observed in DWT method while CWT method gives a better baseline ahape and a well noise suppressed spectrum.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.11 no.4
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• pp.13-19
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• 2012

There are many dynamic properties in measured end-milling force. So, it is difficult to predict the real static property of end-milling force. Also the behavior of end-milling force is very complex to predict with the measured one. To extract the static property from measured force, it must be filtered and its problem is closely related to a de-noising one. Also this paper presents alternative de-noising method of end-milling force using wavelet filter bank, based on the wavelet transform and its inverse one. In this paper, by comparing the measured force and its wavelet filtered one, the fundamental end-milling force property after wavelet transform is well reviewed and analyzed. This result of wavelet filtering with filter bank shows the static force of end-milling which has severe dynamic properties occurring in entry and exit state of edge emersion into the workpiece.

• Speech Sciences
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• v.5 no.1
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• pp.23-33
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• 1999

Mallat has shown that, with a proper choice of wavelet function, the local maxima of wavelet transformed signal indicate a sharp variation in the signal. Since the glottal closure causes sharp discontinuities in the speech signal, dyadic wavelet transform can be useful for detecting abrupt change in the voiced sounds, i.e., epochs. In this paper, we investigate the glottal closure instants obtained from the wavelet analysis of speech signal and compare them with those obtained from the EGG signal. Then, we detect pitch period of speech signal on the basis of these results. Experimental results demonstrated that local maxima of wavelet transformed signal give accurate estimation of epoch and pitch periods of voiced sound obtained by the proposed algorithm also correspond to those from EGG well.

• Computers and Concrete
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• v.2 no.6
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• pp.481-498
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• 2005

A wavelet based approach is proposed for structural damage detection in beams, plate and delamination of composite plates. Wavelet theory is applied here for crack identification of a beam element with a transverse on edge non-propagating open crack. Finite difference method was used for generating a general displacement equation for the cracked beam in the first example. In the second and third example, damage is detected from the deformed shape of a loaded simply supported plate applying the wavelet theory. Delamination in composite plate is identified using wavelet theory in the fourth example. The main concept used is the breaking down of the dynamic signal of a structural response into a series of local basis function called wavelets, so as to detect the special characteristics of the structure by scaling and transformation property of wavelets. In the light of the results obtained, limitations of the proposed method as well as suggestions for future work are presented. Results show great promise of wavelet approach for damage detection and structural health monitoring.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.34S no.3
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• pp.55-62
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• 1997

For the effective removal of artifacts and the extraction of an improved evoked potential response, we propose the averaging method usin gthe shrinkag eof wavelet coefficients. The wavelet analysis decomposes the measured evoked potentials into scale coefficients with low frequency components and wavelet coefficients with high ones as a resolution level, respectively. and in the course of synthesis evoked potentials, the presented method shrinks the wavelet coefficients, and then reproduces the evoked potentials, and lastly averages it. We measured visual evoked potentials to simulate the averaging method using the shrinkage of wavelet coefficients, and compared it with aveaged signal. As a result of simulations, the proposed method gets improved VEP about 0.2-1.6dB in comparison with the averaging method with daubechies wavelet in the resolution level four.

• Journal of Advanced Marine Engineering and Technology
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• v.36 no.5
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• pp.662-673
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• 2012

This study introduces a condition diagnosis technique for a turbine governor system. The governor system is an important control system to handle turbine speed in a nuclear power plant. The turbine governor system includes turbine valves and stop valves which have their own functions in the system. Because a turbine governor system is operated by high oil pressure, it is very difficult to maintain under stable operating conditions. Turbine valves supply oil pressure to the governor system for proper operation. Using the pressure variation of turbine and governor valves, operating conditions of the turbine governor control system are detected and identified. To achieve automatic detection of valve status, time-based and frequency-based analysis is employed. In this study, a new approach, wavelet decomposition, was used to extract specific features from the pressure signals of the governor and stop valves. The extracted features, which represent the operating conditions of the turbine governor system, include important information to control and diagnose the valves. After extracting the specific features, decision rules were used to classify the valve conditions. The rules were generated by a decision tree algorithm (a typical simple method for data-based rule generation). The results given by the wavelet-based analysis were compared to detection results using time- and frequency-based approaches. Compared with the several related studies, the wavelet transform-based analysis, the proposed in this study has the advantage of easier application without auxiliary features.