• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.891-896
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• 1994

Daubechies [1] discoverd compactly supported scaling functions and corresponding wavelets with high regularities. It seems that there are no known compactly supported scaling functions other than Daubechies'. In this article, we will construct new scaling functions supproted in intervals of length $\leq 3$ without using deep analysis. While one of them is Daubechies' scaling function, others are less regular than Daubechies'. Also, we will show that Daubechies' scaling function is the unique one with highest regularity.

• Journal of Electrical Engineering and Technology
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• v.2 no.2
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• pp.172-177
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• 2007

Wavelet transforms provide basis functions for time-frequency analysis and have properties that are particularly useful for the compression of analogue point on wave transient and disturbance power system signals. This paper evaluates the compression properties of the discrete wavelet transform using actual power system data. The results presented in the paper indicate that reduction ratios up to 10:1 with acceptable distortion are achievable. The paper discusses the application of the reduction method for expedient fault analysis and protection assessment.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.1 no.1
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• pp.55-64
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• 1997

We show that if an even length filter has the same length complementary filter in a generalized linear phase case, the complementary filter is unique, we find sufficient conditions for a unique existence of even length N complementary filter in a quadrature mirror filter bank, and we find all higher degree symmetric filters of length N + 4m which are complementary to a given symmetric filter of even length N.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.3
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• pp.21-28
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• 2007

The symmetric dual filters are essential for the construction of biorthogonal multiresolution an analyses and wavelets. We propose an algorithm to seek for dual symmetric trigonometric filters $\tilde{m}_0$ for for the given symmetric trigonometric filter $m_0$ and illustrate our algorithm by examples.

• Bulletin of the Korean Mathematical Society
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• v.61 no.2
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• pp.489-509
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• 2024

In this paper, let q ∈ (0, 1]. We establish the boundedness of intrinsic g-functions from the Hardy-Lorentz spaces with variable exponent H^p(·),q(ℝⁿ) into Lorentz spaces with variable exponent L^p(·),q(ℝⁿ). Then, for any q ∈ (0, 1], via some estimates on a discrete Littlewood-Paley g-function and a Peetre-type maximal function, we obtain several equivalent characterizations of H^p(·),q(ℝⁿ) in terms of wavelets.

• Journal of KIISE:Software and Applications
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• v.29 no.8
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• pp.521-528
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• 2002

We propose a new approach to the feature selection for the classification of handwritten characters using two-dimensional(2D) wavelet packet bases. To extract key features of an image data, for the dimension reduction Principal Component Analysis(PCA) has been most frequently used. However PCA relies on the eigenvalue system, it is not only sensitive to outliers and perturbations, but has a tendency to select only global features. Since the important features for the image data are often characterized by local information such as edges and spikes, PCA does not provide good solutions to such problems. Also solving an eigenvalue system usually requires high cost in its computation. In this paper, the original data is transformed with 2D wavelet packet bases and the best discriminant basis is searched, from which relevant features are selected. In contrast to PCA solutions, the fast selection of detailed features as well as global features is possible by virtue of the good properties of wavelets. Experiment results on the recognition rates of PCA and our approach are compared to show the performance of the proposed method.

• 한국해양학회지
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• v.18 no.2
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• pp.117-124
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• 1983

Pizza's synthetic model, a modified Wiener filter method, was tested to establish the procedure of desirable interpretive wavelet extraction and its application to the marine seismic exploration using several approaches with a real offshore seismic data of the southeast Asia. Noise spectrum acquisition is difficult and any assumptions for it do not produce interpretive wavelets as good as synthetic model result by Piazza (1979). however the resolution could be improved with spiking deconvoultion and following zero phase bandpass filter, and the testing procedure and evaluatttion of results can hopefully contribute in future study and practical evaluation of Piazza's method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.5
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• pp.939-951
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• 2002

We propose a new multiscale Galerkin method based on interpolation wavelets for two-dimensional Poisson's and plane elasticity problems. The major contributions of the present work are: 1) full multiresolution numerical analysis is carried out, 2) general boundaries are handled by a fictitious domain method without using a penalty term or the Lagrange multiplier, 3) no special integration rule is necessary unlike in the (bi-)orthogonal wavelet-based methods, and 4) an efficient adaptive scheme is easy to incorporate. Several benchmark-type problems are considered to show the effectiveness and the potentials of the present approach. is 1-2m/s and impact deformation of the electrode depends on the strain rate at that velocity, the dynamic behavior of the sinter-forged Cu-Cr is a key to investigate the impact characteristics of the electrodes. The dynamic response of the material at the high strain rate is obtained from the split Hopkinson pressure bar test using disc-type specimens. Experimental results from both quasi-static and dynamic compressive tests are Interpolated to construct the Johnson-Cook model as the constitutive relation that should be applied to simulation of the dynamic behavior of the electrodes. The impact characteristics of a vacuum interrupter are investigated with computer simulations by changing the value of five parameters such as the initial velocity of a movable electrode, the added mass of a movable electrode, the wipe spring constant, initial offset of a wipe spring and the virtual fixed spring constant.

• Proceedings of the KSRS Conference
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• 2008.10a
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• pp.169-172
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• 2008

Land-use or land-cover classification of satellite images is one of the important tasks in remote sensing application and many researchers have been tried to enhance classification accuracy. Previous studies show that the classification technique based on wavelet transform is more effective than that of traditional techniques based on original pixel values, especially in complicated imagery. Various wavelets can be used in wavelet transform. Wavelets are used as basis functions in representing other functions, like sinusoidal function in Fourier analysis. In these days, some basis functions such as Haar, Daubechies, Coiflets and Symlets are mainly used in 2D image processing. Selecting adequate wavelet is very important because different results could be obtained according to the type of basis function in classification. However, it is not easy to choose the basis function which is effective to improve classification accuracy. In this study, we computed the wavelet coefficients of satellite image using 10 different basis functions, and then classified test image. After evaluating classification results, we tried to ascertain which basis function is the most effective for image classification. We also tried to see if the optimum basis function is decided by energy parameter before classifying the image using all basis function. The energy parameter of signal is the sum of the squares of wavelet coefficients. The energy parameter is calculated by sub-bands after the wavelet decomposition and the energy parameter of each sub-band can be a favorable feature of texture. The decision of optimum basis function using energy parameter in the wavelet based image classification is expected to be helpful for saving time and improving classification accuracy effectively.

• The KIPS Transactions:PartB
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• v.12B no.7 s.103
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• pp.795-802
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• 2005

In this paper, we present a facial expression recognition-synthesis system that recognizes 7 basic emotion information automatically and renders face with non-photorelistic style in PDA For the recognition of the facial expressions, first we need to detect the face area within the image acquired from the camera. Then, a normalization procedure is applied to it for geometrical and illumination corrections. To classify a facial expression, we have found that when Gabor wavelets is combined with enhanced Fisher model the best result comes out. In our case, the out put is the 7 emotional weighting. Such weighting information transmitted to the PDA via a mobile network, is used for non-photorealistic facial expression animation. To render a 3-D avatar which has unique facial character, we adopted the cartoon-like shading method. We found that facial expression animation using emotional curves is more effective in expressing the timing of an expression comparing to the linear interpolation method.