In this paper, an efficient implementation of the Continuous Flow 2N point Real to Complex FFT is presented. The computation is based on the Radix-2 version of Cooley-Tukey algorithm. The key feature of this implementation is the alternation between DIF (Decimation In Frequency) and DIT (Decimation In Time) in the computation of FFT and IFFT of successive symbols. It allows minimizing the total memory requirement. This method requires only 2*N complex memory locations to perform a 2*N point Real-to-Complex FFT of a continuous data flow when other current methods need 3*N or more. The Real to Complex FFT is computed in two steps: a Complex to Complex FFT then Post-Processing. The Complex to Real IFFT is also computed in two steps: Pre-Processing then a Complex to Complex IFFT. 'Cycle Stealing' allows sharing the clock cycles and the data memory banks between the Complex to Complex FFT/IFFT and the Post/Pre-Processing. Only four memory banks and two physical cells (Butterflies) are used to compute an FFT of up to 8192 real input samples with a computation speed twice as fast as the input data rate. This implementation allows a scalable FFT/IFFT: the same hardware resources are used for different FFT sizes 2*N=2" where (1/spl les/n/spl les/13).