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http://yadda.icm.edu.pl:80/baztech/element/bwmeta1.element.baztech-article-BSW1-0062-0001

Czasopismo

Metrology and Measurement Systems

Tytuł artykułu

Computation of reconstruction function for samples in shift-invariant spaces

Autorzy Zhaoxuan, Z.  Houjun, W.  Zhigang, W. 
Treść / Zawartość http://www.metrology.pg.gda.pl/archives.html http://journals.pan.pl/dlibra/journal/99851
Warianty tytułu
Języki publikacji EN
Abstrakty
EN We address the problem of reconstructing a class of sampled signals which is a member of shift-invariant spaces. In the traditional method, the reconstruction was obtained by first processing the samples by a digital correction filter, then forming linear combinations of generated functions shifted with period T. In order to eliminate the digital correction filter, we propose a computational approach to the reconstruction function. The reconstruction was directly acquired by forming linear combinations of a set of reconstruction functions. The key idea is to obtain a matrix equation by means of oblique frame theory. The reconstruction functions are obtained by solving the matrix equation. Finally, the computational approach is applied, respectively, to reconstruction of a digitizer which samples the signal by derivative sampling or periodically non-uniform sampling technology. The results show that the method is effective.
Słowa kluczowe
EN Hilbert space   shift-invariant spaces   sampling   frame   reconstruction function  
Wydawca Komitet Metrologii i Aparatury Naukowej PAN
Czasopismo Metrology and Measurement Systems
Rocznik 2009
Tom Vol. 16, nr 4
Strony 535--544
Opis fizyczny Bibliogr. 14 poz., rys., wykr., wzory
Twórcy
autor Zhaoxuan, Z.
autor Houjun, W.
autor Zhigang, W.
  • University of Electronic Science and Technology of China, The College of Automation Engineering, Chengdu, Sichuan, 611731, China, zhaoxuanzhu@uestc.edu.cn
Bibliografia
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[10] R. Venkataramani, Y. Bresler: “Perfect reconstruction formulas and bounds on aliasing error in sub-nyquist nonuniform sampling of multiband signals”. IEEE Trans. Inform. Theory, vol. 46, no. 6, Sep. 2000, pp. 2173-2183.
[11] I. Djokovic, P.P. Vaidyanathan: “Generalized sampling theorems in multiresolution subspaces”. IEEE Trans. Signal Process., vol. 45, Mar. 1997, pp. 583-599.
[12] Y.C. Eldar: “Sampling without input constraints: Consistent reconstruction in arbitrary spaces” in Sampling, Wavelets and Tomography, A.I. Zayed and J. J. Benedetto, Eds. Boston, MA: Birkhauser, 2004, pp.33-60.
[13] S. Remani, M. Unser: “Nonideal Sampling and Regularization Theory”. IEEE Trans. Signal Process., vol. 56, no. 3, 2008, pp. 1055-1070.
[14] Y.M. Lu, M.N. Do: “A Theory for Sampling Signals From a Union of Subspaces”. IEEE Trans. Signal Process., vol. 56, no. 6, 2008, pp. 2334-2345.
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