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In this paper, an efficient method for computation of the DFT of a 2N - point real sequence by using DIT FFT with CORDIC based butterflies is presented. Most of the real world applications use long real valued sequences. By using FFT with CORDIC based butterflies, the space required on ROM and also the time required to perform the operation can be reduced. Further, to calculate the 2N - point DFT, by using one N-point DFT involving complex valued data, efficiency is almost doubled.