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Страницы: 130-135.

Язык статьи: Русский.

Аннотация:
Целью настоящей работы является разработка быстрых алгоритмов вычисления так называемых «гиперкомплексных» дискретных преобразований Фурье (ДПФ) и анализ их вычислительных характеристик.

Keywords:
d-dimensional DFT, commutative-associative algebra, fast algorithm, discrete Fourier transforms

Citation:
Aliev MV. Fast algorithms of d-dimensional DFT of real signal in commutativeassociative algebras. Computer optics 2002; 24: 130-135.

Литература:

1. Chernov V.M. Discrete orthogonal transforms with data representation in composition algebras // Proc.of the 9th Scandinavian Conference on Image Analysis (SCIA'95). - Uppsala, Sweden, 1995. V. 1. Р.357-364.
2. Chernov V.M. Arithmetic method in the theory of discrete orthogonal transforms // Proc. SPIE, 1995. V. 2363. Р.134-141.
3. Chichyeva M.A., Pershina M.V. On various schemes of 2D-DFT decomposition with data representation in the quaternion algebra // Image Processing and Communications, Institute of Telecommunications Bydgoszcz, Poland, 1996. Vol. 2. No 1. Р. 13-20.
4. Чернов В.М. Алгоритмы дискретных ортогональных преобразований, реализуемые в кодах Гамильтона-Эйзенштейна // Проблемы передачи информации, 1995. Т.31 N 3. С.38-46.
5. Bülow Th. and Sommer G. Multi-Dimensional Signal Processing Using an Algebraically Extended Signal Representation // Algebraic Frames of Perception- Action Cycle, AFPAC'97, Kiel, Germany, 1997. Р. 148-163.
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7. Bülow Th., Felsberg M. and Sommer G. Noncommuntative Hypercomplex Fourier Transforms of Multidimensional Signals // G. Sommer (Ed.), Geometric Computing with Clifford Algebra, Springer Series in Information Sciences, Springer- Verlag, Berlin, 2001.
8. Felsberg M., Bülow Th. and Sommer G. Commutative Hypercomplex Fourier Transforms of Multidimensional Signals // G. Sommer (Ed.), Geometric Computing with Clifford Algebra, Springer Series in Information Sciences, Springer-Verlag Berlin, 2001.
9. Felsberg M., Bülow Th., Sommer G. and Vladimir M. Chernov. Fast Algorithms of Hypercomplex Fourier Transforms // G. Sommer (Ed.), Geometric Computing with Clifford Algebra, Springer Series in Information Sciences, Springer-Verlag Berlin, 2001.
10. Bülow Th. and Sommer G. Local Hypercomplex Signalrepresentations and Applications // G. Sommer (Ed.), Geometric Computing with Clifford Algebra, Springer Series in Information Sciences, Springer-Verlag Berlin, 2001. Part I , Part II.
11. Felsberg M. and Sommer G. Optimized Fast Algorithms for the Quaternionic Fourier Transform // CAIP'99, Ljubljana, Slovenia, 1999. p. 25-32
12. Felsberg M. and Sommer G. Fast Algorithms for the Hypercomplex Fourier Transforms // WTFB'99, Brandenburg, 1999.
13. Chernov V.M., Bülow Th. and Felsberg M. Synthesis of fast algorithms for discrete Fourier-Clifford transform // Pattern Recognition and Image Analysis, January 1998.
14. Bülow Th. und Sommer G. Das Konzept einer zweidimensionalen Phase unter Verwendung einer algebraisch erweiterten Signalrepräsentation // 19. DAGM Symposium Mustererkennung, Braunschweig, 1997. p. 351-358.
15. Bülow Th. and Sommer G. Algebraically Extended Representations of Multi-Dimensional Signals // Proc. of the 10th Scandinavian Conference on Image alysis, SCIA'97, Lappeenranta, 1997. p. 559- 566.

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