Prime number DFT computation via parallel circular convolvers

A great deal of work has been carried out in recent years into the construction of computationally efficient small discrete Fourier transform (DFT) algorithms. Most small-DFT algorithms exploit the equivalence of prime number DFT computation with that of circular convolution, as well as Winograd´s complexity theory results relating to the optimal computation of small circular convolutions, to achieve reduced-complexity solutions. The paper extends these results to the case of medium/large prime number DFT computation by means of the Agarwal-Cooley technique, (1977), whereby a multidimensional index mapping combined with Winograd´s results, converts the associated one-dimensional circular convolution into a multidimensional nested circular convolution. The resulting computation structure is then expressed in the form of an input addition phase, an output addition phase and, in between, a number of independent circular convolutions, which in hardware can be implemented in parallel, via both word-level and bit-level arithmetic techniques, to provide high-throughput solutions to the original prime number DFT computation