A new group distributed arithmetic design for the one dimensional discrete Fourier transform

This paper presents a new group distributed arithmetic (GDA) design for the one-dimensional discrete Fourier transform (1-D DFT). We adopt the way of Distributed Arithmetic (DA) computation and exploit the good features of the cyclic convolution to facilitate an efficient realization of one-dimensional N-point DFT using ROM module with small size, a barrier shifter, and N accumulators. To increase the ROM utilization, we re-arrange the content of ROM into several groups in which all the elements in a group will be accessed simultaneously in accumulating all the DFT outputs in word-parallel and bit-serial manner. It is called the GDA design approach in this paper. To compare the results with the traditional DA design, the design with the proposed approach can reduce significantly both the hardware cost and the propagation delay.