A systolic array implementation of common factor algorithm to compute DFT

An extension to the common factor algorithm, CFA, to compute discrete Fourier transform, DFT, under the condition that the site of the transform is N=M², shows that the input and output data array of the transform may have identical index mapping. A simple planar 2-dimensional systolic array implementation of CFA algorithm is presented. The systolic array consists of N homogeneous processing element, PE. A DFT of size N=M² can be computed in 2M+1 steps of pipelined operations, achieving the area-time complexity AT² =O(N²log³N). Asymptotically sub-optimal and without the necessity of complicated index mapping and data shuffling, the proposed approach is compared favorably with other existing approaches in realistic VLSI implementation. This architecture has also very good expansibility that a 2^tN-size DFT transform can be computed on 2^t nearest-neighbor connected N-size array with reloaded twiddle factors, which makes it more suitable for VLSI implementation of DFT transform in various practical size