The design of optimal DFT algorithms using dynamic programming

A broad class of efficient discrete Fourier transform algorithms is developed by partitioning short DFT algorithms into factors. The factored short DFT's are combined into longer DFT's using multi-dimensional index maps. By exploiting a property which allows some of the factors to commute, a large set of possible DFT algorithms is generated which contains both the prime factor algorithm (PFA) and the Winograd Fourier transform algorithm (WFTA) as special cases. The problem of finding an algorithm from this class which is optimal with respect to the specific add, multiply, and data transfer characteristics of a particular implementation is posed, and a highly effective dynamic programming algorithm is presented as a solution.