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==Preliminaries==
The concept of a [[Bandlimiting|bandlimited]] function in one dimension can be generalized to the notion of a wavenumber-limited function in higher dimensions. Recall that the [[Fourier transform]] of an integrable function ''ƒ(.)'' on ''n''-dimensional Euclidean space is defined as:
:<math>\hat{f}(\xi) = \mathcal{F}(f)(\xi) = \int_{\Re^n} f(x) e^{-2\pi i \langle x,\xi \rangle} \, dx</math>
where ''x'' and ''ξ'' are ''n''-dimensional [[vector (mathematics)|vectors]], and <math>\langle x,\xi \rangle</math> is the [[inner product]] of the vectors. The function ''ƒ(.)'' is said to be wavenumber-limited to a set <math>\Omega</math> if the Fourier transform satisfies <math>\hat{f}(\xi) = 0</math> for <math>\xi \notin \Omega</math>.
Similarly, the configuration of uniformly spaced sampling points in one-dimension can be generalized to a [[lattice]] in higher dimensions. A lattice is a collection of points <math>\Lambda \subset \Re^n</math>
<math>
\Lambda = \left\{ \sum_{i=1}^n a_i v_i \; | \; a_i \in\Bbb{Z} \right\}
</math>
where {''v''<sub>1</sub>, ..., ''v''<sub>''n''</sub>} is a [[Basis (linear algebra)|basis]] for <math>\Re^n</math>. The [[reciprocal lattice]] <math>\Gamma</math> corresponding to <math>\Lambda</math> is defined by
:<math>
\Gamma = \left\{ \sum_{i=1}^n a_i u_i \; | \; a_i \in\Bbb{Z} \right\}
</math>
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