Discrete orthogonal transforms such as the discrete Fourier transform, discrete cosine\ntransform, discrete Hartley transform, etc., are important tools in numerical analysis, signal processing,\nand statistical methods. The successful application of transform techniques relies on the existence of\necient fast algorithms for their implementation. A special place in the list of transformations is\noccupied by the discrete fractional Fourier transform (DFrFT). In this paper, some parallel algorithms\nand processing unit structures for fast DFrFT implementation are proposed. The approach is based\non the resourceful factorization of DFrFT matrices. Some parallel algorithms and processing unit\nstructures for small size DFrFTs such as N = 2, 3, 4, 5, 6, and 7 are presented. In each case, we describe\nonly the most important part of the structures of the processing units, neglecting the description of\nthe auxiliary units and the control circuits.
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