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

Realization of N-point Discrete Fourier Transform (DFT) using one-dimensional or two-dimensional systolic array structures have 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 into smaller lengths. Triple matrix product form of representation enables to map the Npoint DFT on a 2-D systolic array. In this work, an algorithm is developed and is mapped to a 2dimensional systolic structure where DFT size can be non-power of two. The proposed work gives flexibility to choose N for an application where N is a composite number. The total time required to compute N-point DFT is 2(N1-1)+N2+N for any N=N1N2. The array can be used for matrix-matrix multiplication and also to compute the diagonal elements of triple-matrix multiplication for various 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.