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Efficient Fast Hartley Transform Algorithms for HypercubeConnected Multicomputers \Lambda

Summary: Efficient Fast Hartley Transform Algorithms for
Hypercube­Connected Multicomputers \Lambda
Cevdet Aykanat, member, IEEE, and Argun Dervis›
Department of Computer Engineering, Bilkent University
06533 Bilkent, Ankara, Turkey
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 an 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 medium­to­coarse grain hypercube multicom­
puters by introducing a dynamic mapping scheme for the restructured FHT. The proposed
parallel algorithm achieves perfect load­balance, minimizes both the number and volume of
concurrent communications, allows only nearest­neighbor communications and achieves in­
place computation and communication. The proposed algorithm is implemented on a 32­node
iPSC/2 1 hypercube multicomputer. High efficiency values are obtained even for small size
FHT problems.
Index Terms : Digital Signal Processing, Fast Hartley Transform, parallel computing, multi­


Source: Aykanat, Cevdet - Department of Computer Engineering, Bilkent University


Collections: Computer Technologies and Information Sciences