The fast Fourier transform its role as an algebraic algorithm
John D. Lipson · 1976
In the past decade the Cooley-Tukey fast Fourier transform (FFT) [1] has achieved the status of a “super” algorithm. As a numerical (complex field) algorithm, the FFT has revolutionized large scale time series analysis in a way that counts most—economic. (See, e.g., Refs. 3-6.) Since the late sixties, the FFT has also emerged as an important algebraic(abstract field) algorithm, with many interesting applications to the theory and practice of algebraic computing. The abstract character of the FFT, in particular its role as an algebraic algorithm, is what this paper is about.