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Efficient Fast Hartley Transform Algorithms for Hypercube-Connected Multicomputers
June 1995 (vol. 6 no. 6)
pp. 561-577

Abstract—Although fast Hartley transform (FHT) provides efficient spectral analysis of real discrete signals, the literature that addresses the parallelization of FHT is extremely rare. FHT is a real transformation and does not necessitate any complex arithmetics. On the other hand, FHT algorithm has an irregular computational structure which makes efficient parallelization harder. In this paper, we propose a efficient restructuring for the sequential FHT algorithm which brings regularity and symmetry to the computational structure of the FHT. Then, we propose an efficient parallel FHT algorithm for medium-to-coarse grain hypercube multicomputers by introducing a dynamic mapping scheme for the restructured FHT. The proposed parallel algorithm achieves perfect load-balance, minimizes both the number and volume of concurrent communications, allows only nearest-neighbor communications and achieves in-place computation and communication. The proposed algorithm is implemented on a 32-node iPSC/21 hypercube multicomputer. High-efficiency values are obtained even for small size FHT problems.

Index Terms—Digital signal processing, fast Hartley transform, parallel computing, multicomputer, hypercube, load balance, nearest-neighbor communication.

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Cevdet Aykanat, Argun Dervi\c s, "Efficient Fast Hartley Transform Algorithms for Hypercube-Connected Multicomputers," IEEE Transactions on Parallel and Distributed Systems, vol. 6, no. 6, pp. 561-577, June 1995, doi:10.1109/71.388039
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