Solution to the indexing problem of multidimensional DFT´s on arbitrary sampling lattices

A method for implementing the indexing step of multidimensional FFTs is presented. The initial arrangement of the multidimensional data bears a heavy effect on the rearranging of the data. The proposed method seeks an appropriate geometry for the data which allows partial decoupling between the different dimensions. The result is a set of linear integer equations which is solved using the Smith normal factorization of the periodicity matrix. The hexagonal indexing algorithm is given as an illustration.