On the nested FFT algorithm

A new technique, which transforms the DFT into cyclic convolutions and additions, is combined with fast algorithms for cyclic convolution and the Kronecker product to compute a specific category of prime factor DFTs of size N, where N has a power-of-2 factor and other relatively prime factors. The new algorithm uses a nested computation structure in which there is only one stage of multiplication and all multipliers are nested inside additions. The method is compared with other algorithms in terms of the number of multiplications and additions. With its new factorization techniques, the method requires fewer multiplications than the WFTA in some cases. Accordingly, the nested algorithm which includes the WFTA is extended as it is not limited any more to compute DFTs of size N, where N has a power-of-2 factor not greater than 16.