||In this seminar, I will compare some sampling and aliasing properties of three three-dimensional sampling grids: the face-centered cubic, the body-centered cubic and the cubic point-lattices.
The Fourier transform of a point-lattice V is the reciprocal of V. If the Fourier transform of a signal in spatial domain is zero outside the Voronoi region of this reciprocal point-lattice, then the signal can be completely reconstructed. If not, the reconstructed signal is corrupted by aliasing. By numerical integration in frequency domain, the part of the signal that gives aliasing (i.e., that is not contained the Voronoi region in the reciprocal lattice) can be computed. By using this property, the sampling efficiency of the different lattices are compared.