Symmetric prime factor fast fourier transform algorithms

The prime factor algorithm (PFA) is a fast algorithm for the evaluation of the discrete Fourier transform (DFT), applicable when the sequence length N is a product of relative primes. PFAs are presented that take advantage of the symmetry in a real-even or real-odd sequence. These algorithms require only one-fourth the real arithmetic and storage requirements of the complex PFA. As with existing state-of-the-art PFAs, these algorithms can be performed in-place and in-order.