New algorithms for the FFT computation of symmetric and translational complex conjugate sequences

A previously proposed algorithm for the FFT (fast Fourier transform) computation of real symmetric and antisymmetric sequences reduced the N-point symmetric FFT computation to a N/4-point complex FFT computation, but the postprocessing involved division by sin(2πk/N). For large size N, this may cause stability problems. An algorithm is presented which overcomes the problem for real symmetric and antisymmetric data sequences. A similar algorithm is given for the translational complex conjugate symmetric data sequence