Very fast computation of the radix-2 discrete Fourier transform

Abstract

This paper develops and presents a radix-2 fast Fourier transform (FFT) algorithm that reduces the computational effort (as measured by the number of multiplications) to two-thirds of the effort required by most radix-2 algorithms. The resulting algorithm is similar to one obtained by applying a principle suggested by Rader and Brenner; however, its structure is particularly appealing when transforming pure real or imaginary sequences and/or symmetric or antisymmetric sequences; furthermore, memory requirements (other than those for storing the input data) do not grow with the size of the transform.