• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.723-737
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• 2010

In this paper, we investigate the sampling theorem for frame in multiwavelet subspaces. By the frame satisfying some special conditions, we obtain its dual frame with explicit expression. Then, we give an equivalent condition for the sampling theorem to hold in multiwavelet subspaces. Finally, a sufficient condition under which the sampling theorem holds is established. Some typical examples illustrate our results.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.195-203
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• 2009

In this paper, a necessary and sufficient condition for lattice sampling theorem to hold for frame in subspaces of $L^2$(R) is established. In addition, we obtain the formula of lattice sampling function in frequency space. Furthermore, by discussing the parameters in Theorem 3.1, some corresponding corollaries are derived.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.351-358
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• 2007

For an entire function f whose Fourier transform has a compact support confined to $[-{\pi},\;{\pi}]$ and restriction to ${\mathbb{R}}$ belongs to $L^2{\mathbb{R}}$, we derive a nonuniform sampling theorem of Lagrange interpolation type with sampling points ${\lambda}_n{\in}{\mathbb{R}},\;n{\in}{\mathbb{Z}}$, under the condition that $$\frac{lim\;sup}{n{\rightarrow}{\infty}}|{\lambda}_n-n|<\frac {1}{4}$.

• Communications of the Korean Mathematical Society
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• v.17 no.4
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• pp.731-740
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• 2002

We derive the generalized Hermite interpolation by using the contour integral and extend the generalized Hermite interpolation to obtain the sampling expansion involving derivatives for band-limited functions f, that is, f is an entire function satisfying the following growth condition ｜f(ｚ)｜$\leq$ A exp($\sigma$｜y｜) for some A, $\sigma$ > 0 and any ｚ=$\varkappa$ + iy∈C.

• Proceedings of the IEEK Conference
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• 1998.06a
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• pp.46-49
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• 1998

In this paper, we introduce the notion of intelligent communication by introducing a novel intelligent receiver model. This receiver is continually evolving and learns and improves in performance as it compiles its experience over time. In digital communication context, in a typical training mode, it jearns the concept of "1" as is deteriorated by arbitrary (not necessarily additive as is typically assumed) disturbance and /or modulation. After learning "1", in test mode, it classifies the received signal "1" and "0" almost completely. The intelligent receiver as implemented is grounded on the recently introduced Stochastic Morphological Sampling Theorem(SMST), a distribution-free result which gives theoretical bounds on the sample complexity(training size) needed for the required performance parameters such as accuracy($\varepsilon$) and confidence($\delta$). Based on this theorem, we demonstrate --almost irrespective of channel and modulation model-- the number of samples needed to learn the concept of "1" is not too "large" and the resulting universal receiver structure, that corresponding to classical Nearest Neighbor rule in Pattern Recognition Theory, is trivial. We check the surprising efficiency and validity of this model through some simple simulations. and validity of this model through some simple simulations.

• The Transactions of the Korean Institute of Power Electronics
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• v.3 no.4
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• pp.338-345
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• 1998

The mathematical interpretation of a practical sampler which is useful to obtain the small signal models for the peak and average current mode controls is proposed. Due to the difficulties in applying the Shannons sampling theorem to the analysis of sampling effects embedded in the current mode control, several different approaches have been reported. However, these approaches require the information of the inductor current in a discrete expression, which restricts the application of the reported method only to the peak current mode control. In this paper, the mathematical expressions of sampling effects on a current loop which can directly apply the Shannons sampling theorem are newly proposed, and applied to the modeling of the peak current mode control. By the newly derived models of a practial smapler, the models in a discrete time domain and a continuous time domain are obtained. It is expected that the derived models are useful for the control loop design of power supplies. The effectiveness of the derived models are verified through the simulation and experimental results.

• Journal of the Earthquake Engineering Society of Korea
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• v.7 no.4
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• pp.81-87
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• 2003

In this paper, the feasibility of using Shannon's sampling theorem to reconstruct exact mode shapes of a structural system from a limited number of sensor points and localizing damage in that structure with reconstructed mode shapes is investigated. Shannon's sampling theorem for the time domain is reviewed. The theorem is then extended to the spatial domain. To verify the usefulness of extended theorem, mode shapes of a simple beam are reconstructed from a limited amount of data and the reconstructed mode shapes are compared to the exact mode shapes. On the basis of the results, a simple rule is proposed for the optimal placement of accelerometers in modal parameter extraction experiments. Practicality of the proposed rule and the extended Shannon's theorem is demonstrated by detecting damage in laboratory beam structure with two-span via applying to mode shapes of pre and post damage states.

• Journal of the Korean Mathematical Society
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• v.47 no.6
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• pp.1299-1316
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• 2010

We derive estimates for the truncation, amplitude and jitter type errors associated with Hermite-type interpolations at equidistant nodes of functions in Paley-Wiener spaces. We give pointwise and uniform estimates. Some examples and comparisons which indicate that applying Hermite interpolations would improve the methods that use the classical sampling theorem are given.

• Proceedings of the KIPE Conference
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• 1998.07a
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• pp.275-278
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• 1998

The mathematical interpretation of a practical sampler which is useful to obtain the small signal models for the peak and average current mode controls is proposed. Due to the difficulties in applying the Shannon's sampling theorem to the analysis of sampling effects embedded in the current mode control, several different approaches have been reported. However, these approaches require the information of the inductor current in a discrete expression, which restricts the application of the reported method only to the peak current mode control. In this paper, the mathematical expressions of sampling effects on a current loop which can directly apply the Shannon's sampling theorem are newly proposed, and applied to the modeling of the peak current mode control. By the newly derived models of a practical sampler, the models in a discrete time domain and a continuous time domain are obtained. It is expected that the derived models are useful for the control loop design of power supplies. The effectiveness of the derived models are verified through the simulation and experimental results.