Numerical Analysis: A fast fourier transform algorithm for real-valued series

Abstract

A new procedure is presented for calculating the complex, discrete Fourier transform of real-valued time series. This procedure is described for an example where the number of points in the series is an integral power of two. This algorithm preserves the order and symmetry of the Cooley-Tukey fast Fourier transform algorithm while effecting the two-to-one reduction in computation and storage which can be achieved when the series is real. Also discussed are hardware and software implementations of the algorithm which perform only ( N /4) log ₂ ( N /2) complex multiply and add operations, and which require only N real storage locations in analyzing each N -point record.