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sampling theorem and digital electron microscopy

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Progress in Natural Science:Materials International 1997年第1期 112-116页

作者：彭练矛 Beijing 100080 Beijing Laboratory of Electron Microscopy China Chinese Academy of Sciences

The sampling problem is important in digital electron microscopy which deals with discrete digital micrographs. In recording a digital electron micrograph using a digital CCD camera, the camera size is usually limited to less than 1024 ×1024. This limitation results mainly *** consideration of the cost of the CCD camera and the exposure time needed to record the digital mi-

关键词： digital electron microscopy sampling theorem imaging processing FFT.

EXACT EVALUATIONS OF FINITE TRIGONOMETRIC SUMS BY sampling theoremS

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Acta Mathematica Scientia 2011年第2期31卷 408-418页

作者： M.H. Annaby R.M. Asharabi Department of Mathematics Faculty of Science Cairo University Department of Mathematics Faculty of Education Al-MahweetSana'a University

We use the sampling representations associated with Sturm-Liouville difference operators to derive generalized integral-valued trigonometric sums. This extends the known results where zeros of Chebyshev polynomials of the first kind are involved to the use of the eigenvalues of difference operators, which leads to new identities. In these identities Bernoulli＇s numbers play a role similar to that of Euler＇s in the old ones. Our technique differs from that of Byrne-Smith （1997） and Berndt-Yeap （2002）.

关键词： Trigonometric sums difference equations sampling theorem

sampling formulas for 2D quaternionic signals associated with various quaternion Fourier and linear canonical transforms

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Frontiers of Information Technology & Electronic Engineering 2022年第3期23卷 463-478页

作者： Xiaoxiao Hu Dong CHENG Kit Ian KOU The First Affiliated Hospital of Wenzhou Medical University Wenzh.ou Medical UniversityWenzhou 325000China Research Center for Mathematics and Mathematics Education Beijing Normal University(Zhuhai)Zhuhai 519087China Department of Mathematics Faculty of Science and TechnologyUniversity of MaoouMacaoChina

The main purpose of this paper is to study different types of sampling formulas of quaternionic functions,which are bandlimited under various quaternion Fourier and linear canonical *** show that the quaternionic bandlimited functions can be reconstructed from their samples as well as the samples of their derivatives and Hilbert *** addition,the relationships among different types of sampling formulas under various transforms are ***,if the quaternionic function is bandlimited to a rectangle that is symmetric about the origin,then the sampling formulas under various quaternion Fourier transforms are *** this rectangle is not symmetric about the origin,then the sampling formulas under various quaternion Fourier transforms are different from each ***,using the relationship between the two-sided quaternion Fourier transform and the linear canonical transform,we derive sampling formulas under various quaternion linear canonical ***,truncation errors of these sampling formulas are ***,some simulations are provided to show how the sampling formulas can be used in applications.

关键词： Quaternion Fourier transforms Quaternion linear canonical transforms sampling theorem Quaternion partial and total Hilbert transforms Generalized quaternion partial and total Hilbert transforms Truncation errors

ON TRUNCATION ERROR BOUND FOR MULTIDIMENSIONAL sampling EXPANSION LAPLACE TRANSFORM

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Analysis in Theory and Applications 2004年第1期20卷 52-57页

作者： LongJingfan BeijingNormalUniversity China

The truncation error associated with a given sampling representation is defined as the difference between the signal and on approximating sumutilizing a finite number of terms. In this paper we give uniform bound for truncation error of bandlimited functions in the n dimensional Lebesgue space Lp(Rn) associated with multidimensional Shannon sampling representation.

关键词： truncation error band limited function sampling theorem

An Almost Sure Result on Approximation of Homogeneous Random Field from Local Averages

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Chinese Journal of Electronics 2019年第1期28卷 93-99页

作者： SONG Zhanjie ZHANG Shuo School of Mathematics Tianjin University Department of Mathematics Tianjin University of Finance and Economics

The problem of approximation of homogeneous random field from asymmetric local average sampling is considered in this paper. As a general sampling result, a sufficient condition is obtained to ensure the homogeneous random field be approximated from local averages with probability 1, which extended the result for weak sense stochastic process from local averages to homogeneous random field.

关键词： sampling theorem Homogeneous random field Local averages sampling

Improvement of FEM's dynamic property

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Applied Mathematics and Mechanics(English Edition) 2010年第11期31卷 1337-1346页

作者：江增荣段鹏飞郭杏林丁桦 The Second Research Department Equipment Research Institute of PLA's Second Artillery Institute of Mechanics Chinese Academy of Sciences Department of Engineering Mechanics Dalian University of Technology

The discretization size is limited by the sampling theorem, and the limit is one half of the wavelength of the highest frequency of the problem. However, one half of the wavelength is an ideal value. In general, the discretization size that can ensure the accuracy of the simulation is much smaller than this value in the traditional finite element method. The possible reason of this phenomenon is analyzed in this paper, and an efficient method is given to improve the simulation accuracy.

关键词： sampling theorem efficiency finite element discretization macro element condensation method deformation modification dispersion relationship

Four-band compactly supported orthogonal symmetric interpolating scaling function

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Progress in Natural Science:Materials International 2001年第4期11卷 63-70页

作者：水鹏朗保铮 China Key Laboratory for Radar Signal Processing Xi an 710071 Xidian University

An efficient method is proposed to design 4-band scaling functions with the following five advantages : compact support, orthogonality, symmetry, regularity, and interpolation; and a family of such scaling functions w... 详细信息

关键词： sampling theorem scaling function interpolation symmetry.

N-widths on the classes of multivariate bandlimited functions

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Progress in Natural Science:Materials International 2004年第10期14卷 23-26页

作者： FANG Gensun and LONG Jingfan (Department of Mathematics,Beijing Normal University,Beijing100875,China) Received January30,2004 Beijing Normal Univ Dept Math Beijing 100875 Peoples R China

In this paper,the tight order on the n-widths of the classes of multivariate bandlimited functions in L p ( d ),1

关键词： n-width multivariate bandlimited function sampling theorem

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基于FPGA的串行总线测试系统设计

基于FPGA的串行总线测试系统设计