The fast Hartley transform on the hypercube multiprocessors

The Fast Hartley Transform is a promising alternative to the Fast Fourier Transform when the processed data are real numbers. The hypercube implementation of the FHT is largely dependent on the way the computation is partitioned. A partitioning algorithm is presented which generates evenly-loaded tasks on each node and demands only a regular communication topology — the Hartley graph. Mapping from the Hartley graph to the Gray graph (binary n-cube) is straightforward, since the Hartley graph has a similar structure as the Gray graph. However, the communication is not always between the nearest neighbors and thus may take some extra time. Moreover, the slowness of the communication in the presently available architectures imposes a limitation on the speedup when a large number of processors are used.