A hybrid algorithm for the rapid Fourier transform of extensive series of data

Abstract

A technique is described for the rapid Fourier transform of large series of numbers. The technique takes advantage of the fact that most digital series are highly factorizable by the number 2, which permits the use of the F.F.T. algorithm. Using two magnetic tape units, or alternatively magnetic disk facilities, very large series can be transformed efficiently with only modest computer facilities. For the transformation of odd-valued series the Thomas Prime-Factor and Gentleman and Sande algorithms are treated in detail.