A Fast Fourier Transform Algorithm for Real-Valued Series
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-Turkey 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) log2 (N/2) complex
multiply and add operations, and which require 
only N real storage locations in analyzing each N-point record.
CACM October, 1968
Bergland, G. D.
