Factored-matrix representation of distributed fast transforms
Bainbridge, Richard Lee
Kirk, Donald E.
Therrien, Charles W.
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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 parallel 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 later-processor data transfers on the Butterfly Network. The properties of there "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.
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