Two-dimensional nonuniform sampling expansions an iterative approach. i. theory of two-dimensional bandlimited signals
作者： Paul L. Butzer , Guido Hinsen
DOI: 10.1080/00036818908839838
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摘要: The major aim is to establish a nonuniform sampling theorem for two-dimensional functions bandlimited parallelogram centered at the origin by an iterative application of one-dimensional expansion formulae. For this purpose results on square integrable are given, and inequality S.M. Nikol'skii samples taken equally spaced nodes generalized case. A first version desired derived here; main ones follow in Part II
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sci-hub.se 参考文章(17)
Jacques Arsac, Fourier Transforms and the Theory of Distributions ,(1966)
Farokh A. Marvasti, A Unified Approach to Zero-Crossings and Nonuniform Sampling of Single and Multidimensional Signals and Systems ,(1987)
Norman Levinson, Gap and Density Theorems ,(1940)
Norbert Wiener, Raymond Edward Alan Christopher Paley, Fourier Transforms in the Complex Domain ,(1934)
J. R. Higgins, Five short stories about the cardinal series Bulletin of the American Mathematical Society. ,vol. 12, pp. 45- 89 ,(1985) , 10.1090/S0273-0979-1985-15293-0
J. Higgins, A sampling theorem for irregularly spaced sample points (Corresp.) IEEE Transactions on Information Theory. ,vol. 22, pp. 621- 622 ,(1976) , 10.1109/TIT.1976.1055596
Daniel P. Petersen, David Middleton, Sampling and reconstruction of wave-number-limited functions in N-dimensional euclidean spaces Information & Computation. ,vol. 5, pp. 279- 323 ,(1962) , 10.1016/S0019-9958(62)90633-2
P.L. Butzer, G. Hinsen, Reconstruction of bounded signals from pseudo-periodic, irregularly spaced samples Signal Processing. ,vol. 17, pp. 1- 17 ,(1989) , 10.1016/0165-1684(89)90068-6
W. Splettstosser, Sampling approximation of continuous functions with multidimensional domain (Corresp.) IEEE Transactions on Information Theory. ,vol. 28, pp. 809- 814 ,(1982) , 10.1109/TIT.1982.1056561
E. T. Whittaker, XVIII.—On the Functions which are represented by the Expansions of the Interpolation-Theory Proceedings of the Royal Society of Edinburgh. ,vol. 35, pp. 181- 194 ,(1915) , 10.1017/S0370164600017806