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[[Image:Hexagonal_sampling_lattice.png|thumb|Fig. 1: A hexagonal sampling lattice <math>\Lambda</math> and its basis vectors ''v''<sub>1</sub> and ''v''<sub>2</sub>|right|200px]]
[[Image:Reciprocal_lattice.png|thumb|Fig. 2: The reciprocal lattice <math>\Gamma</math> corresponding to the lattice <math>\Lambda</math> of Fig. 1 and its basis vectors ''u''<sub>1</sub> and ''u''<sub>2</sub> (figure not to scale).|right|200px]]
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 <math>
:<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 <math>f(\cdot)</math> 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>.
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