• Journal of the Korean Mathematical Society
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• v.51 no.5
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• pp.941-953
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• 2014

In this paper, a 2-circular matrix theory is developed, and a concept of spectral radius for biorthogonal wavelet is introduced. We propose a novel design method by minimizing the spectral radius and obtain a wavelet which has better performance than the famous 9-7 wavelet in terms of image compression coding.

• Journal for History of Mathematics
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• v.12 no.1
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• pp.65-72
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• 1999

In this article, we give a historical referencing overview and compressed illuminating procedure of deriving the repersentors R$_y$(x) in Reproducing Kernel space W$^2_2$(R), being needed to find the solutions of integral equations, which construct the wavelets in L$^2$(1R).

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.81-91
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• 2001

The expansion of a distribution of $K^r_M^r(R)$ in terms of regular orthogonal wavelets is considered. The expansion of a distribution of $K^r_M^r(R)$ is shown to converge pointwise to the value of the distribution where is exists.

• Journal of the Korean Mathematical Society
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• v.49 no.2
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• pp.325-342
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• 2012

It is well-known that the m-th order cardinal B-spline wave-let, $\psi_m$, decays exponentially. Our aim in this paper is to determine the exact rate of this decay and thereby to describe the asymptotic behaviour of $\psi_m$.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.199-209
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• 2003

When a sampling theorem holds in wavelet subspaces, sampling expansions can be a good approximation to projection expansions. Even when the sampling theorem does not hold, the scaling function series with the usual coefficients replaced by sampled function values may also be a good approximation to the projection. We refer to such series as hybrid sampling series. For this series, we shall investigate the local convergence and analyze Gibbs phenomenon.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.147-147
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• 2000

Recently, a considerable amount of attention is being given to the use of wavelets and neural network for modulation and equalization. We proposed a new scheme of equalization for constellation using discrete wavelet transform(DWT) and neural network. The DWT is used for noise reduction and the neural network is used to update the equalizer coefficients adaptively.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.10 no.6
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• pp.935-950
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• 1999

A multiresolution time-domain analysis scheme is derived for the analysis of microwave structures by using Haar wavelets to discretize the Maxwell's curl equation. This technique requires less computational effort than the conventional FDTD method because larger space grid can be used in the simulations. To validate this scheme, several 2-D·3-D microwave structures are simulated and the results are compared with those of the conventional FDTD scheme.

• Proceedings of the IEEK Conference
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• 2002.06d
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• pp.385-388
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• 2002

This paper proposes a new GSC (Generalized Sidelobe Canceller) structure, called HLMS-GSC. Compared to Griffiths and Jim's GSC structure, the number of complex multiplication required is reduced to one half. The simulation results show that the minimum mean square errors and performance of nulling jammers by using HLMS-GSC are almost the same compared to Griffiths and Jim's GSC, although the complexity is reduced significantly. As a result, the proposed adaptive beamformer is good for real time implementation, since it has low complexity compared to previous GSC structures.

• Proceedings of the IEEK Conference
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• 2002.06d
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• pp.389-392
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• 2002

This paper propose a new GSC (Generalized Sidelobe Canceller) structure, called HFLMS-GSC. The number of complex multiplication required is reduced to one half compared to FLMS-GSC. The simulation results show that mean square error converging and jamming signal removing characteristics are almost the same compared to FLMS-GSC, although the complexity is reduced significantly. As a result, the proposed structure is good for real time implementation, since it has low complexity compared to previous GSC structures.

• Communications of the Korean Mathematical Society
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• v.13 no.1
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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.