Factored-Matrix Representation of Distributed Fast Transforms.
NAVAL POSTGRADUATE SCHOOL MONTEREY CA
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Parallel implementations of Fast Fourier Transforms FFTs and other fast transforms are represented using factored, partitioned matrices. The factored matrix description of a distributed FFT is introduced using a decimation in time DIT FFT algorithm suitable for implementation on a distributed signal processor. The heart of the matrix representation of distributed fast transforms is the use of permutations of an NxN identity matrix to describe the required interprocessor data transfers on the Butterfly Network. The properties of these transfer matrices and the resulting output ordering are discussed in detail. the factored matrix representation is then used to show that the Fast Hartley Transform FHT and the Walsh Hadamard Transform WHT are supported by the Butterfly Network. Keywords Fast Fourier Transform Fast Hartley Transform Walsh-Hadamard Transform Parallel Processing Distributed Signal Processor Butterfly Network Theses.
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