When the time series being Fourier analyzed or Fourier synthesized consists of solely real numbers, the computa- A Radix-Eight Fast tion and storage requirements of complex fast Fourier Fourier Trarmsf orm ings can be made by forming and analyzing an artificial Subroutine for Real- eliminates the operations that are redundant for real
G. D. Bergland, Bell Telephone · 1969
The algorithm described here is a modification and extension of the latter approach. By allowing a slightly more involved indexing pattern, an algorithm is developed which permits in-place reordering, and can be conveniently extended to an arbitrary-radix algorithm. Radix-eight fast Fourier analysis (FFA) and fast Fourier synthesis (FFS) subroutines making use of this algorithm are given in the Appendix. The FFA subroutine evaluates the equation