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In [[digital signal processing]], '''multidimensional ghg sampling''' is the process of converting a function of a multidimensional variable into a discrete collection of values of the function measured on a discrete set of points. This article presents the basic result due to Petersen and Middleton<ref name="petmid62">D. P. Petersen and D. Middleton, "Sampling and Reconstruction of Wave-Number-Limited Functions in N-Dimensional Euclidean Spaces", Information and Control, vol. 5, pp. 279–323, 1962.</ref> on conditions for perfectly reconstructing a [[wavenumber]]-limited function from its measurements on a discrete [[Lattice (group)|lattice]] of points. This result, also known as the '''Petersen–Middleton theorem''', is a generalization of the [[Nyquist–Shannon sampling theorem]] for sampling one-dimensional [[band-limited]] functions to higher-dimensional [[Euclidean space]]s.
In essence, the Petersen–Middleton theorem shows that a wavenumber-limited function can be perfectly reconstructed from its values on an infinite lattice of points, provided the lattice is fine enough. The theorem provides conditions on the lattice under which perfect reconstruction is possible.
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