Parallel Computing for the Radix-2 Fast Fourier Transform

The fast Fourier transform (FFT) is a speed-up technique for calculating the discrete Fourier transform (DFT), which in turn is a discrete version of the continuous Fourier transform. The Fast Fourier Transform is used in linear systems analysis, antenna studies, optics, random process modeling, probability theory, quantum physics, and boundary-value problems, and has been very successfully applied to restoration of astronomical data. This paper formulates the one dimensional and two dimensional continuous and discrete Fourier transform, especially the fast Fourier transform, considers their parallel algorithms and reports the speed up of parallel computing in both shared memory and distributed memory modes.