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Algorithms of two-dimensional hypercomplex discrete Fourier transform

M.V. Aliev1, A.M. Belov2, A.V. Ershov3,M.A. Chicheva4
1Adyghe State University 

2Samara State Aerospace University 

3Samara State University 

4Image Processing Systems Institute of RAS 


 PDF, 11 kB

Pages: 102-105.

Abstract:
The paper considers the methods of parallel computation of multidimensional hypercomplex discrete Fourier transform. The main idea is to use the properties of the hypercomplex algebra, in which this transform is performed. The natural parallelism of the multidimensional Cooley-Tukey scheme provides additional opportunities for improving the efficiency of the algorithm.

Keywords:
two-dimensional hypercomplex, Fourier transform, parallel computation, hypercomplex algebra, Cooley-Tukey scheme.

Citation:
Aliev MV, Belov AM, Ershov AV, Chicheva MA. Algorithms of two-dimensional hypercomplex discrete Fourier transform. Computer Optics 2004; 26: 102-105.

References:
  1. 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. 
  2. Aliev MV, Chicheva MA. Algorithms of two-dimensional DFT with data representation in hypercomplex algebra. Algebra and linear optimization [In Russian]. Proc Int Seminar Dedicated to the 90th Anniversary of S.N. Chernikov 2002: 18-26. 
  3. Furman YA, Krevetskii AV, Peredereev AK. Introduction to contour analysis. Applications for image and signal processing [In Russian]. Moscow: "Fizmatlit" Publisher; 2002. 
  4. Sommer G, ed. Geometric computing with Clifford algebra. Berlin: Springer-Verlag; 2001. 
  5. Labunets EV, Labunets VG, Egiazarian K, Astola J. Hypercomplex moments application in invariant image recognition. Proc 1998 Int Conf on Image Processing (ICIP98) 1998: 256-261.

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