(27) * << * >> * Russian * English * Content * All Issues

Multidimensional hypercomplex DFT: parallel approach

M.V. Aliev1 M.A. Chicheva 2
1Adygea State University
2Image Processing Systems Institute of RAS

 PDF, 121 kB

Pages: 135-137.

Full text of article: Russian language.

The paper suggests a method for the parallel computation ofhypercomplex numbers in multidimensional space. In particular, a parallel algorithm for the computation of multidimensional hypercomplex discrete Fourier transform (HDFT) is proposed.

DFT, hypercomplex numbers, multidimensional space, Fourier transform.

Aliev MV, Chicheva MA. Multidimensional hypercomplex DFT: parallel approach. Computer Optics 2005; 27: 135-137.

This work was supported by the Russian-American program Basic Research and Higher Education (BRHE); and the Russian Foundation for Basic Research (RFBR), projects No. 03-01-00736, 05-01-96501.


  1. Aliev MV, Belov AM, Ershov AV, Chicheva MA. Algorithms of two-dimensional hypercomplex discrete Fourier transform [In Russian]. Computer Optics 2004; 26: 101-104.
  2. Furman YaA, Krevetsky AV, Peredreev AK. Introduction to contour analysis and its applications to image and signal processing [In Russian]. Moscow: "Fizmatlit" Publisher; 2002.
  3. Sommer G. Geometric computing with Clifford algebras. Berlin, Heidelberg: Springer-Verlag; 2001. ISBN: 978-3-540-41198-7.
  4. Vanwormhoudt MC. Rings of hypercomplex numbers for NT Fourier transforms. Signal Process 1998; 67(2): 189-198. DOI: 10.1016/S0165-1684(98)00036-X.
  5. Bülow T, Sommer G. Hypercomplex signals – A novel extension of the analytic signal to the multidimensional case. IEEE Trans Signal Process 2001; 49(11): 2844-2852. DOI: 10.1109/78.960432.
  6. Chaitelin F, Meškauskas T. Computation with hypercomplex numbers. Nonlinear Anal Theory Methods Appl 2001; 47(5): 3391-3400. DOI: 10.1016/S0362-546X(01)00454-0.
  7. Labunets EV, Labunets VG, Egiazarian K, Astola J. Hypercomplex moments application in invariant image recognition. Proceedings 1998 International Conference on Image Processing (ICIP98) 1998; 2: 257-261. DOI: 10.1109/ICIP.1998.723359.
  8. Sommer G. A geometric algebra approach to some problems of robot vision. In Book: Byrnes J, ed. Computational noncommutative algebra and applications. Dordrecht: Springer; 2004: 309-338. DOI: 10.1007/1-4020-2307-3_11.
  9. Aliev MV. Fast algorithms of d-dimensional DFT of real signal in commutative-associative algebras of 2D dimensionality over the real number field [In Russian]. Computer Optics 2002; 24: 130-136.
  10. Gupta A, Kumar V. The scalability of FFT on parallel computers. IEEE Trans Parallel Distrib Syst 1993; 4(8): 922-932. DOI: 10.1109/71.238626.
  11. Inda MA, Bisseling RH. A simple and efficient parallel FFT algorithm using the BSP model. Parallel Comput 2001; 27(14): 1847-1878. DOI: 10.1016/S0167-8191(01)00118-1.

© 2009, IPSI RAS
151, Molodogvardeiskaya str., Samara, 443001, Russia; E-mail: ko@smr.ru ; Tel: +7 (846) 242-41-24 (Executive secretary), +7 (846) 332-56-22 (Issuing editor), Fax: +7 (846) 332-56-20