Grioryan Fft and Cooley-tukey Fft onto Xilinx Virtex-ii pro and Virtex-5 Fpgas

A large family of signal processing techniques consist of Fourier-transforming a signal, manipulating the Fourier-transformed data in a simple way, and reversing the transformation. We widely use Fourier frequency analysis in equalization of audio recordings, X-ray crystallography, artefact removal in Neurological signal and image processing, Voice Activity Detection in Brain stem speech evoked potentials, speech processing spectrograms are used to identify phonetic sounds and so on. 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 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 [3] and Virtex-5 [4] FPGAs, by developing our own FFT processor architectures. Finally we show that the Grigoryan FFT is working fatser than Cooley-Tukey FFT, consequently it is useful for higher sampling rates. Operating at higher sampling rates is a challenge in DSP applications.