Authors' summary: ``The fast Fourier transform, Good-Winograd Fourier transform and Winograd Fourier transform are studied using residue arithmetic. High speed, high precision arithmetic is achieved by using arithmetic architecture and a plurality of small wordlength processors running in parallel. The disadvantage of this arithmetic is overflow intolerance. To ensure that register overflow will not occur, in this modular structure, scaling policies for the three discrete Fourier transforms are derived and compared.''