Discrete Fourier transform algorithms for real valued sequences

It is well known that the discrete Fourier transformation (DFT) of a real-valued sequence contains some redundancies. More precisely, approximately half of the DFT coefficients suffice to completely determine the DFT. In this paper, it is shown that the choice of the set of (nonredundant) DFT coefficients to be calculated affects the efficiency of the resulting algorithm. One especially interesting choice is discussed in detail for the case of mixed radix-(2, 3) DFT algorithms. Algorithms for the DFT calculation of both one and more dimensional real-valued arrays are discussed.