There are alternatives to the Cooley-Tukey FFT which can serve the same or related purposes and which can have advantages in certain situations . Examples include the fast discrete cosine transform (DCT) , discrete Hartley transform , number theoretic transform , prime factor algorithm (PFA) [34,42,8,81],A.10and the Winograd Fourier transform . A tutorial review of fast Fourier transform algorithms (1990) is given in .A.11
The DCT, used extensively in image coding, is described in §A.6.1 below. The Hartley transform, optimized for processing real signals, does not appear to have any advantages over a ``pruned real-only FFT'' . The number theoretic transform has special applicability for large-scale, high-precision calculations (see §A.6.2 below). The PFA and Winograd transform are closely related, with the PFA being somewhat faster .