An efficient FFT algorithm for real-symmetric data

A very efficient algorithm for computing the discrete Fourier transform (DFT) of real-symmetric input is presented. The algorithm is based on Bruun´s algorithm where, except for the last stage, all twiddle factors are purely real. It is well-known that about half of the arithmetic operations and memory requirements can be removed when the input is real-valued. It may be assumed that another half of the computational and memory requirements can be eliminated when the input is real and symmetric. This is, however, impossible with a standard radix-2 fast Fourier transform (FFT), but can be achieved by the Bruun algorithm. The symmetries within the algorithm with for real-symmetric input are exploited to remove about three fourths of the butterflies and memory locations. The algorithm presented achieves the same low arithmetic as the split-radix FFT for real-symmetric data, but has a structure that is as simple as the radix-2. The implementation on the TMS320C30 shows that the new algorithm fits a DSP processor very well. The program requires 0.51-0.60 ms to compute a length 1024 FFT with real-symmetric data