Implementation of FFT by using MATLAB: SIMULINK on Xilinx Virtex-4 FPGAs: Performance of a Paired Transform Based FFT

Discrete Fourier Transform is principal mathematical method f or the frequency analysis and is having 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 giv es 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 i s 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 - 4 FPGAs [3], by developing our own FFT processor architectures. Finally we show that the Grigo ryan FFT is working faster than Cooley - Tukey FFT, consequently it is useful for higher sampling rates. Operating at higher sampling rates is a challenge in DSP applications