On the application of the number theoretic methods of high-speed convolution to two-dimensional filtering

The Fermat number transform has been proposed as an aid to the rapid and precise computation of convolutions for digital filtering applications, but because it is less flexible than the fast Fourier transform, while more efficient, its applicability to one-dimensional filtering situations is somewhat limited. The purpose of this letter is to call attention to the fact that the constraints associated with filtering by Fermat number transforms are far less restrictive for two-dimensional filtering, and that, in fact, the Fermat number transform is well matched to the requirements of two-dimensional linear filtering.