Powiadomienia systemowe
- Sesja wygasła!
- Sesja wygasła!
- Sesja wygasła!
Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
The paper deals with some new algorithms for "overlapped" calculation of 1D and 2D DFT spectra of a multi-channel sognal. The algorithms' computational complexity is decreased via a fast calculation of an auxiliary transform that takes values in special algebraic structures: the group algebra of a quaternion units group and the algebra associated with integral Hurwitz quaternions.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
139--151
Opis fizyczny
Bibliogr. 18 poz.
Twórcy
autor
- Image Proceeding Systems Institute (IPSI RAS), 151 Molodogvardejskaya St, 443001, Samara, Russia
Bibliografia
- [1] Hurwitz A.: Uber die Zahlentheorie der QuaLernionen. Nach. Gesellschaft Wiss. Gottingen. Math.-Phys. Klasse, 313-340. 1896.
- [2] Hall M.: The Theory of Groups. The McMillan Company. NY. 1959.
- [3] Coxeter H. S.: Twelve Geometric Essays. Southern Illinois Press, Carbondale IL. 1968.
- [4] Tits J.: Quaternions over Q (V5), Leech's Lattice and the Sporadic Group of Hall-Janko. J. Algebra, 63, 56-75. 1980.
- [5] Elliot D. F. , Rao K. R.: Fast Transforms. Academic, NY. 1982.
- [6] Blahut R. E.: Fast Algorithms for Digital Signal Processing. Addison-Wesley. 1985.
- [7] Conway J. H., Sloan N. J .A.: Sphere Packing, Lattices and Groups. Springer. 1988.
- [8] Chernov V. M.: Arithmetic methods in the theory of discrete orthogonal transforms. Proc. SPIE., 2363, 134-141. 1994.
- [9] Porteous I. R.: Clifford Algebras and Cllasical Groups. Cambridge. 1995.
- [10] Chernov V. M.: Parametrization of some classes of fast algorithms for discrete orthogonal transforms (1) PR&IA, 5 (2), 238-245. 1995.
- [11] Chernov V. M.: Discrete orthogonal transforms with data representation in composition algebras. Proc. of The 9th Sc. Conf. IA, Uppsala, Sweden, 1, 357-364. 1995.
- [12] Sangwine S. J.: Fourier transforms of color images using quaternion, or hypercomplex, numbers. Electronics Letters, 32 (21), 1979-198O. 1996.
- [13] Chichyeva M. A., Pershina M. V.: On various schemes of 2D-DFT decompositoion with data representation in the quaternion algebra. Image Processing and Communications, 2(1), 13-20. 1996.
- [14] Tolimieri R., An Myoung, Lu Chao: Mathematics of Multidimensional Fourier Transform. Springer. 1997.
- [15] Tolimieri R., An Myoung, Lu Chao: Algorithms for Discrete Fourier Transform and Convolution. Springer. 1997.
- [16] Buelow T., Sommer G.: Multi-Dimensional Signal Processing Using an Algebraically Extended Signal Representation. Sommer G., Koenderink J. J. (Eds.). Algebraic Frames for Perception-Action Cycle, Springer, LNCS 1395, l48-163. 1997.
- [17] Chernov V. M., Buelow T., Felsberg M.: Synthesis of fast algorithm for discrete Fourier-Clifford transform . PR&IA, 8 (2), 274-275. 1998.
- [18] Chernov V. M.: Clifford Algebras as Projections of Group Algebras. E. Bayro-Corrochano, G. Sobczyk (Eds.): Advanches in Geometric Algebra with Applications in Science and Engineering, Birkhauser, Boston, 467-482. 2001.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BWA1-0002-0061