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The paper presents the in-place implementation of the multidimensional radix 2 fast Fourier transform (FFT), along with the corresponding algorithm for data shuffling (bit-reversal) on SIMD hypercube computers. Each processor possesses its own non-shared memory, the number of processors being less than or equal to the number of data. The flexibility of the proposed algorithm is based on the scheme of information storage that has been chosen and in the decomposition/configuration of the hypercube in subhypercubes that allow the parallel processing of multiple one-dimensional FFTs. This parallel FFT algorithm has an optimum performance, since the data redundancy is and the algorithmic complexity is optimum.