ON THE REDUCTION OF MULTIDIMENSIONAL DFT TO SEPARABLE DFT BY SMITH NORMAL-FORM THEOREM

The growing applications of image and image-sequence processing call f or the computation of the discrete Fourier transform (DFT) of multidim ensional signals defined on lattices of general type. The multidimensi onal DFT formula, introduced by Mersereau, allows one to choose the fr equency domain sampling lattice, which is not univocally determinated by the signal definition lattice. On the other hand, the consistency o f the inverse multidimensional DFT formula has been taken for granted in the general case. This work presents a proof based on the Smith nor mal form theorem.