PAIRED FASTER FFT: GRIGORYAN FFT IMPLEMENTATION AND PERFORMANCE ON XILINX FPGAS AND TMS DSPS

Discrete Fourier Transform is a principal mathematical method for the frequency analysis and has wide applications in Engineering and Sciences. Because the DFT is so ubiquitous, fast methods for computing DFT have been studied extensively, and continuous to be an active research. The way of splitting the DFT gives out various fast algorithms. In this paper, we present the implementation of two fast algorithms for the DFT for evaluating their performance. One of them is the popular radix-2 Cooley-Tukey fast Fourier transform algorithm (FFT) [1] and the other one is the Grigoryan FFT based on the splitting by the paired transform [2]. We evaluate the performance of these algorithms by implementing them on the Xilinx Virtex-II Pro [6], Virtex-4[9] and Virtex-5[7] FPGAs, by developing our own FFT processor architectures. We have evaluated the performances also by implementing on Texas Instruments fixed point DSP processors: TMS320C5416[17], TMS320C6748[17], TMS320C5515[17]. Finally we show that the Grigoryan FFT is working faster than the Cooley-Tukey FFT, consequently it is useful for higher sampling rates. Operating at higher sampling rates is a challenge in DSP applications. We proved that on Xilinx FPGAs and TMS DSPs, the Grigoryan FFT is performing at most 1.358 and 1.7 times faster than the Cooley-Tukey FFT respectively. We also confirm that for the same architectures Virtex-5 platform is better platform for implementing the Grigoryan FFT