This paper proposes novel CORDIC-based systolic arrays for the computation of discrete Fourier transform (DFT) and discrete Hartley transform (DHT) for radix-2 length sequences. While maintaining the local data communication requirement, the redundancy in the computation of DFT and DHT is reduced to an optimum level. As a result, the number of processing elements required are reduced to a minimum. The proposed arrays are regular in nature and enjoy the advantages of parallelism, pipelined nature, modularity, regularity, local interconnections and synchronized multiprocessing. The proposed arrays, we believe, will be highly useful for real-time signal processing applications.