ISSN:
1573-0824
Keywords:
Shannon and Kramer sampling theorems inN dimensions
;
anN-dimensional Paley-Wiener interpolation theorem for band-limited signals and multidimensional Lagrange interpolation
Source:
Springer Online Journal Archives 1860-2000
Topics:
Electrical Engineering, Measurement and Control Technology
Notes:
Abstract Kramer's sampling theorem, which is a generalization of the Whittaker-Shannon-Kotel'nikov (WSK) sampling theorem, enables one to reconstruct functions that are integral transforms of types other than the Fourier one from their sampled values. In this paper, we generalize Kramer's theorem toN dimensions (N ≥ 1) and show how the kernel function and the sampling points in Kramer's theorem can be generated. We then investigate the relationship between this generalization of Kramer's theorem andN-dimensional versions of both the WSK theorem and the Paley-Wiener interpolation theorem for band-limited signals. It is shown that the sampling series associated with this generalization of Kramer's theorem is nothing more than anN-dimensional Lagrange-type interpolation series.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01940228
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