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Consider two uniform samplers operating simultaneously on a signal, with sample spacings MT and NT where M and N are coprime integers, and T has time or space dimension. It can be shown that the difference coarray of this pair of sampling arrays has elements at all integer multiples of T, regardless of how large M and N are. This implies that any application which depends only on second order statistics, such as angle of arrival estimation, beamforming, and multiple frequency detection, can be carried out at high resolution with the help of sparse sampling arrays. One manifestation is that two sensor arrays withM and N sensors can actually identify O(MN) independent sources. This paper extends these results to the case of multidimensional signals. The multidimensional sampling arrays operate on a lattice geometry. The coarray of such a system is studied. Even though the two lattice arrays are sparse (with respect to the integer grid), the coarray contains all integer vectors. It is also shown how to achieve the effect of a high resolution multidimensional DFT filter bank by combining coprime low resolution filter banks.