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This work describes the design and implementation issues of the Fast Wavelet Packet Transform (FWPT) 1D and 2D on a parallel distributed memory multiprocessors. In particular, we describe two different approaches in the development of a parallel implementation of the FWPT of a matrix A. In section 2 we introduce some notations and definitions, in section 3 we describe the computational environments, and, in section 4, we discuss the parallel implementation of the bidimensional FWPT. In section 4.3 we finally show a numerical experiment.