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 , and number theoretic transform .
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 (§A.6.2 below).