Abstract
Sampling series expansions for functions (signals) that are bandlimited to N-dimensional rectangles ( N ≥ 1) have been studied extensively; however, if a function is bandlimited to a general region in R N , not much is known about its sampling series expansion. In this paper, we derive a sampling theorem for functions that are bandlimited (in the sense of Kramer) to finite regions with smooth boundaries in R N . The sampling series expansions obtained for these functions are Lagrange-type interpolation series. Our technique utilizes Green′s function of the region involved. As an application of our sampling theorem, we obtain a new method for summing infinite series in several variables.
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