Triple-Matrix Product-Based 2D Systolic Implementation of Discrete Fourier Transform

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Realization of $$N$$N-point discrete Fourier transform (DFT) using one-dimensional or two-dimensional systolic array structures has been developed for power of two DFT sizes. DFT algorithm, which can be represented as a triple-matrix product, can be realized by decomposing $$N$$N into smaller lengths. Triple-matrix product form of representation enables to map the $$N$$N-point DFT on a 2D systolic array. In this work, an algorithm is developed and is mapped to a two-dimensional systolic structure where DFT size can be non-power of two. The proposed work gives flexibility to choose $$N$$N for an application where $$N$$N is a composite number. The total time required to compute $$N$$N-point DFT is $$2(N_{1}-1)+N_{2}+N$$2(N1-1)+N2+N for any $$N=N_{1}N_{2}$$N=N1N2. The array can be used for matrix---matrix multiplication and also to compute the diagonal elements of triple-matrix multiplication for other applications. The proposed architecture produces in-order stream of DFT sequence at the output avoiding need for reordering buffer. Large sized DFT can be computed by repeatedly using the proposed systolic array architecture.