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Sampling expansions for discrete transforms and their relationship with interpolation series. (English) Zbl 0918.65087

In sampling theory, integral transforms are recovered from their values at discrete sequences of points. Kramer’s sampling theorem gives the possibility to reconstruct integral transforms from their values at sequences of real numbers. It is known that this theorem includes the Whittaker- Shannon-Kotel’nikov (WSK) sampling theorem, and that many Kramer-type expansions can be written in form of Lagrange-type interpolation series.
Here the author introduces a discrete version of Kramer’s theorem and proves that the discrete theorem is equivalent to Kramer’s theorem. The WSK sampling theorem is shown to be included in the new theorem. Moreover, the relationship between the sampling expansion of the discrete transforms and the interpolation expansions is discussed.
Reviewer: R.S.Dahiya (Ames)

MSC:

65R10 Numerical methods for integral transforms
44A15 Special integral transforms (Legendre, Hilbert, etc.)
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