• 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.

• 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.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.379-385
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• 2014

For a bandlimited function with polynomial growth on the real line, we derive a nonuniform sampling expansion using a special bandlimited function which has polynomial decay on the real line. The series converges uniformly on any compact subsets of the real line.

• 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.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.17 no.6
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• pp.69-78
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• 2017

Shannon of the 5G smartphone and Fourier of the signal processing meet in the sampling theorem (2 times the highest frequency 1). In this paper, the initial Shannon Theorem finds the Shannon capacity at the point-to-point, but the 5G shows on the Relay channel that the technology has evolved into Multi Point MIMO. Fourier transforms are signal processing with fixed parameters. We analyzed the performance by proposing a 2N-1 multivariate Fourier-Jacket transform in the multimedia age. In this study, the authors tackle this signal processing complexity issue by proposing a Jacket-based fast method for reducing the precoding/decoding complexity in terms of time computation. Jacket transforms have shown to find applications in signal processing and coding theory. Jacket transforms are defined to be $n{\times}n$ matrices $A=(a_{jk})$ over a field F with the property $AA^{\dot{+}}=nl_n$, where $A^{\dot{+}}$ is the transpose matrix of the element-wise inverse of A, that is, $A^{\dot{+}}=(a^{-1}_{kj})$, which generalise Hadamard transforms and centre weighted Hadamard transforms. In particular, exploiting the Jacket transform properties, the authors propose a new eigenvalue decomposition (EVD) method with application in precoding and decoding of distributive multi-input multi-output channels in relay-based DF cooperative wireless networks in which the transmission is based on using single-symbol decodable space-time block codes. The authors show that the proposed Jacket-based method of EVD has significant reduction in its computational time as compared to the conventional-based EVD method. Performance in terms of computational time reduction is evaluated quantitatively through mathematical analysis and numerical results.

• Journal of Broadcast Engineering
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• v.20 no.3
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• pp.398-407
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• 2015

Compressive sensing (CS) has drawn much interest as a novel sampling technique that enables sparse signal to be sampled under the Nyquitst/Shannon rate. By noting that the block-based CS can still keep spatial correlation in measurement domain, this paper proposes to adapt sampling rate of each block in frame according to its characteristic defined by edge information. Specifically, those blocks containing more edges are assigned more measurements utilizing block-wise correlation in measurement domain without knowledge about full sampling frame. For natural image, the proposed adaptive rate allocation shows considerable improvement compared with fixed subrate block-based CS in both terms of objective (up to 3.29 dB gain) and subjective qualities.

• Journal of Korea Multimedia Society
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• v.20 no.7
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• pp.1004-1013
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• 2017

This paper presents a relationship between the number of curves and geometric parameters of a 3D object. Once the relationship is established, the number of closed curves that can reliably represent 3D object is derived. Inspired by Shannon-Nyquist Sampling Theorem, in this paper, approach for sampling rate (defined as the minimum number of curves) for 3D reconstruction is proposed. The relationship is straightforward, is suitable for application to 3D object overlaid with closed-continuous curves, and can achieve efficient 3D reconstruction system in practice. To substantiate the proposed approach, simulation results are provided and the results show that the number of curves can be decreased without loss of generality of characteristics of a target 3D object.

• Horticultural Science & Technology
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• v.32 no.1
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• pp.84-90
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• 2014

Berchemia racemosa var. magna is only found in Anmyeon Island of South Korea. Genetic diversity and the spatial genetic structure of B. racemosa var. magna in Anmyeon Island were studied by I-SSR marker system. Fifty I-SSR amplicons were produced from 8 selected primers. We used 13 polymorphic markers to analyze the genetic structure. Distribution of 39 individuals in the study plot($90m{\times}70m$) showed aggregate pattern (aggregation index = 0.706). Total 21 genets were observed from 39 individuals through I-SSR genotyping. Proportion of distinguishable genotype (G/N), genotype diversity (D) and genotype evenness (E) were 53.8%, 0.966 and 0.946, respectively. In spite of the small number and the narrow distribution, Shannon's diversity index (I = 0.598) was relatively high as compared with those of the other plant species. For ex situ genetic conservation of B. racemosa var. magna, the sampling strategy based on spatial autocorrelation using Tanimoto distance is efficient at choosing the conserved individuals with a 6 meter interval between individual trees.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.67 no.7
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• pp.898-902
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• 2018

A novel heart beat interval estimation algorithm is presented based on parabola approximation method. This paper presented a two-step processing scheme; a first stage is finding R-peak in the Electrocardiogram (ECG) by Shannon energy envelope estimator and a secondary stage is computing the interpolated peak location by parabola approximation. Experimental results show that the proposed algorithm performs better than with the previous method using low sampled ECG signals.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2014.06a
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• pp.230-231
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• 2014

Compressive sensing is a new sampling technique, which allows to sample a signal under the Nyquist-Shannon sampling rate. For block-based compressive sensing, a hybrid sensing matrix which contains low-frequency patterns in addition to the random Gaussian numbers is good for exploiting typical property of natural images. By noting that MH-BCS-SPL is well known for its good recovery performance, this paper investigates effect of the hybrid sensing matrix on MH-BCS-SPL in the sense of how large portion of low-frequency patterns can provide performance improvement.