• Journal of applied mathematics & informatics
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• 제28권3_4호
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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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• 제27권1_2호
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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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• 제12권1_2호
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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.

• 대한수학회보
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• 제44권2호
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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}$.

• 대한수학회논문집
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• 제17권4호
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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.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 1998년도 하계종합학술대회논문집
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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.

• 전력전자학회논문지
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• 제3권4호
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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.

• 한국지진공학회논문집
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• 제7권4호
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• pp.81-87
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• 2003

본 논문에서는 Shannon의 샘플링 이론을 이용하여 제한된 수의 센서에서 얻은 모드형상으로 정확한 모드형상을 재생성하고, 이렇게 재생성한 모드형상을 이용하여 구조물에 발생한 손상을 탐지할 수 있는지의 가능성에 대해 조사하였다. 우선 시간 영역에서의 Shannon의 샘플링 이론을 검토하였고, 이를 공간영역으로 확대하였다. 공간영역으로 확대한 Shannon의 샘플링 이론은 그 효용성을 확인하기 위하여 단순보의 모드형상을 해석적으로 구한 후 최소한으로 제한된 수의 샘플 데이터로 모드형상을 재생하였고 이를 원래의 모드형상과 비교하였다. 이렇게 하여 얻은 결과를 바탕으로 구조물의 모드형상을 추출하는 동적실험에서 필요한 최적 가속도계의 위치를 구할 수 있는 간단한 관계식을 제안하였다. 제안된 관계식과 공간영역으로 확대한 Shannon의 샘플링 이론의 실용성은 연속 2스팬으로 구성된 실험실 빔 구조물의 손상 전과 후의 모드형상에 적용하여 손상을 탐지함으로써 입증하였다.

• 대한수학회지
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• 제47권6호
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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.

• 전력전자학회:학술대회논문집
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• 전력전자학회 1998년도 전력전자학술대회 논문집
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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.