New realisation technique of high-speed discrete Fourier transform described by distributed arithmetic

This paper presents the results of a study using distributed arithmetic on a microprocessor to implement a prime-number-based discrete Fourier transform (DFT). The matrix equation of the DFT can be reordered in a convolution form suitable for distributed arithmetic. Further simplification of the equation can be achieved by noting some simple properties of number theory and the DFT. It was found that the total computation time for a 61-point DFT, using a 2 MHz clock 6800 microprocessor, was only 3.6 ms, and the computation time increases directly in proportion to the number of points in the DFT. This fast realisation technique should be suitable both for microprocessor-based systems and for the direct hardware implementation.