A relationship between the structures of the radix-2 DIT FHT and complex-valued FFT algorithms

By reformulating the existing radix-2 decimation-in-time (DIT) FHT and complex-valued FFT algorithms using an efficient index mapping, a close relationship between the two algorithms is established. A detailed comparison between the two algorithms is carried out. It is shown that these algorithms have similar structures and can be implemented using the same butterfly. In view of this relationship and the fact that the DHT is an efficient alternative to the DFT for real data, it should be possible to use a single software or hardware module to compute the DHT as well as the forward and inverse complex-valued DFTs.