Digital filtering using pseudo fermat number transforms

In this paper pseudo Fermat number transforms (FNT´s) are discussed. These transforms are defined in a ring of integers modulo an integer submultiple of a pseudo Fermat number, and can be computed without multiplications while allowing a great flexibility in word length selection. Complex pseudo FNT´s are then introduced and are shown to relieve some of the length limitations of conventional Fermat number transforms (FNT´s). These transforms, which under certain conditions can be computed via fast transform algorithms allow the implementation of digital filters with better efficiency and accuracy than the fast Fourier transform (FFT).