Abstract
The Whittaker-Shannon-Kotel'nikov sampling theorem provides sampling series expansions for the re-construction of functions (signals) that are bandlimited to finite closed intervals, symmetric about the origin, i.e., intervals of type [−a,a]. There are generalizations of this theorem to Ndimensions, yet they all mainly deal with functions that are also bandlimited to N-dimensional rectangles symmetric about the origin. No general theory seems to exist for functions that are bandlimited to a general domain in Ndimensions. In this paper we give, by using polar coordinates, a sampling series expansion that can be used for the reconstruction of functions (signals) that are bandlimited to a disc centered at the origin. The sample points are the eigenvalues of a Dirichlet problem in the disc.
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