The paper shows how novel one-dimensional and two-dimensional systolic processing architectures, comprising up toNcoordinate rotation digital computer (CORDIC) processing elements (PEs), can be used to carry out hardware-efficient parallel implementations of theN-point discrete Fourier transform (DFT), offering highly attractive throughput rates in relation to the conventionalN-processor linear systolic array. The CORDIC PE is implemented in bit-serial form using single-bit half-adder (HA) and full-adder (FA) circuits. It is thus extremely efficient, in terms of speed/area product and possesses simple interconnects, facilitating the mapping of potentially thousands of such units onto a single chip.