 Cooley–Tukey) and removing the redundant parts of the computation, saving roughly a factor of two in time and memory.Alternatively, it is possible to express an "even"-length real-input DFT as a complex DFT of half the length (whose real and imaginary parts are the even/odd elements of the original real data), followed by O("N") post-processing operations.It was once believed that real-input DFTs could be more efficiently computed by means of the discrete Hartley transform (DHT), but it was subsequently argued that a specialized real-input DFT algorithm (FFT) can typically be found that requires fewer operations than the corresponding DHT algorithm (FHT) for the same number of inputs.