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A decimation-in-time radix-2 fast Fourier transform (FFT) algorithm is considered here for implementation in multiprocessors with shared bus, multistage interconnection network (MIN), and in mesh connected computers. Results are derived for data allocation, interprocessor communication, approximate computation time, and speedup of an N point FFT on any P available processing elements (PE's). Further generalization is obtained for a radix-r FFT algorithm. An N X N point two-dimensional discrete Fourier transform (DFT) implementation is also considered when one or more rows of the input data matrix are allocated to each PE.