Implementation of the DFT using radix-2 and paired transform algorithms

Frequency analysis plays 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 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 TMS320C5416 DSP processor 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.