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Discretization of Multidimensional Analog Data: Finite Spectra and Limited Length Fields. Pp. 108–113.

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Section: Physics. Mathematics. Informatics

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519.6.65 + 621.391

Authors

Svinyin Sergey Fyodorovich, St. Petersburg Institute for Informatics and Automation of the Russian Academy of Sciences, 

Vlasenko Yuri Sergeevich, Northern (Arctic) Federal University named after M.V. Lomonosov, Institute of Mathematics and Computer Sciences, 

Konovalov Mikhail Alexandrovich, Russian Institute of Radionavigation and Time, 

Popov Alexander Igorevich, Northern (Arctic) Federal University named after M.V. Lomonosov, Institute of Information and Space Technologies

Abstract

The article considers accuracy evaluations of recovery of multidimensional fields on samples on the basis of the theory of function approximation by systems of polynomial basis splines with various orders. In the context of multidimensional functions with bounded supports there arises a problem of estimation of loss of information due to the use of multidimensional analogues of the discrete Kotelnikov-Shannon model. One of the main causes of sampling errors is infinity of signal spectra.

Keywords

multidimensional signal, finite function, discretization, mesh nodes, recovery, basis spline, finite energy, effective area of spectrum.

The full-text version of the article can be requested through the university’s library.