Letter: On the reduction of multidimensional DFT to separabile DFT by smith normal form theorem
Riccardo Bernardini, Roberto Manduchi · European Transactions on Telecommunications · 1994
Abstract The growing applications of image and image‐sequence processing call for the computation of the discrete Fourier transform (DFT) of multidimensional signals defined on lattices of general type. The multidimensional DFT formula, introduced by Mersereau, allows one to choose the frequency domain sampling lattice, which is not univocally determinated by the signal definition lattice. On the other hand, the consistency of the inverse multidimensional DFT formula has been taken for granted in the general case. This work presents a proof based on the Smith normal form theorem.