Abstract
There are two ways, other than the standard fast Fourier transform (FFT) algorithm, of computing Fourier transforms of real data, namely, (1)the real fast Fourier transform (RFFT) algorithm, and (2) the fast Hartley transform (FHT) algorithm. On a sequential computer, it has been shown that both the RFFT and the FHT algorithms are faster than the FFT algorithm. However, it is not obvious that the same is true on a parallel machine. The communication requirements of the RFFT and the FHT algorithms, which are critical to the cost of any parallel implementation, are different from those of the FFT algorithm. In this paper we present efficient implementations of the RFFT and the FHT algorithms on a hypercube machine. Experimental results are given for the implementation of the RFFT and the FHT algorithms on the NCUBE machine.
Similar content being viewed by others
References
Bailey, D. H. (1987). A high-performance fast Fourier transform algorithm for the CRAY-2,J. Supercomput. 1, 43–60.
Bracewell, R. N. (1986).The Hartley Transform, Oxford University Press, Oxford.
Bergland, G. D. (1968). A fast Fourier transform algorithm for real-valued series,Commun. ACM 11(10), 703–710.
Buneman, O. (1986). Conversion of FFT's to fast Hartley transforms,SIAM J. Sci. Stat. Comput.7(2), 624–638.
Chamberlain, R. M. (1988). Gray codes, fast Fourier transforms and hypercubes,Parallel Comput. 6, 225–233.
Rabiner, L. R., and Gold, B. (1975).Theory and Application of Digital Signal Processing, Prentice-Hall, Englewood Cliffs, New Jersey.
Hockney, R. W., and Jesshope, C. R. (1981).Parallel Computers, Adam Hilger.
Jamieson, L. H., Mueller, P. T., and Siegel, H. J. (1986). FFT algorithm for SIMD parallel processing systems,J. Parallel Distributed Comput. 3, 48–71.
Kamin, R. A., III, and Adams, G.B., III (1988). Fast Fourier transform algorithm design and tradeoffs on the CM-2, in Proceedings of the Conference on Scientific Applications of the Connection Machine, September 1988, pp. 134–160.
Sorensen, H. V., Jones, D. G., Heideman, M. T., and Burrus, C. S. (1987). Real-valued fast Fourier transform algorithms,IEEE Trans. ASSP ASSP-35(6), 849–863.
Swartztrauber, P. N. (1986). Symmetric FFTs,Math. Comput. 47(175), 323–346.
Swarztrauber, P. N. (1987). Multiprocessor FFTs,Parallel Comput. 5, 197–210.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Dubey, A., Zubair, M. & Grosch, C.E. Computing the Fourier transform of real data on a hypercube. J Sci Comput 5, 293–309 (1990). https://doi.org/10.1007/BF01063119
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01063119