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The paper discusses a novel systolic implementation of the row-column method for solving the prime factor discrete Fourier transform (DFT) algorithm. It deals, in particular, with the two-factor decomposition where the transform length N is an odd multiple of 4. By processing the four-point row-DFTs coefficient by coefficient, rather than DFT by DFT, as is conventionally done, it is seen how pipelined implementations of the row-DFT and column-DFT processes can be performed simultaneously, without need for matrix transposition of the row-DFT output, resulting in a fully pipelined concurrent solution. Hardware efficiency and simplicity is achieved via the computationally attractive Cordic (co-ordinate digital computer) arithmetic, with O(N) throughput requiring (asymptotically) one-quarter of the hardware requirements of established N-processor solutions.