On Sampling a High-Dimensional Bandlimited Field on a Union of Shifted Lattices

We study the problem of sampling a high-dimensional bandlimited field on a union of shifted lattices under certain assumptions motivated by some practical sampling applications. Under these assumptions, we show that simple necessary and sufficient conditions for perfect reconstruction can be identified.We also obtain an explicit scheme for reconstructing the field from its samples on the various shifted lattices. We illustrate our results using examples.