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).