Performances of Texas Instruments DSP and Xilinx FPGAs for Cooley-Tukey and Grigoryan FFT Algorithms

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Frequency analysis plays a vital role in the applications like cryptanalysis, steganalysis, system identification, controller tuning, speech recognition, noise filters, etc. Discrete Fourier transform (DFT) is a principal mathematical method for the frequency analysis. 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 (FFT) algorithm and the other one is the Grigoryan FFT based on the splitting by the paired transform. We evaluate the performance of these algorithms by implementing them on the TMS320C5416 DSP and also on the Virtex-II FPGAs. Finally, we show that the paired-transform-based algorithm of the FFT is faster than the radix-2 FFT; consequently, it is useful for higher sampling rates. We also discuss the performances of TMS DSP and Xilinx FPGAs and tradeoffs.