 Bruun's algorithm (above) is another method that was initially proposed to take advantage of real inputs, but it has not proved popular.There are further FFT specializations for the cases of real data that have even/odd symmetry, in which case one can gain another factor of roughly two in time and memory and the DFT becomes the discrete cosine/sine transform(s) (DCT/DST).Instead of directly modifying an FFT algorithm for these cases, DCTs/DSTs can also be computed via FFTs of real data combined with O("N") pre- and post-processing.