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Zracjonalizowany algorytm mnożenia dwóch kwaternionów

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Warianty tytułu
EN
Rationalized algorithm for two quaternion multiplication
Języki publikacji
PL
Abstrakty
PL
W pracy został przedstawiony syntezowany przez autorów zracjonalizowany algorytm mnożenia dwóch kwaternionów wymagający w najbardziej ogólnym przypadku wykonania mniejszej liczby operacji mnożenia w stosunku do bezpośredniego, naiwnego sposobu liczenia.
EN
The rationalized algorithm for two quaternion multiplication which require in the common case of a fewer number of multiplication operations then naive way of computing is presented.
Rocznik
Strony
137--140
Opis fizyczny
Bibliogr. 23 poz., rys., tab.
Twórcy
autor
autor
  • Zachodniopomorski Uniwersytet Technologiczny w Szczecinie, Wydział Informatyki, ul. Żołnierska, 49, 71-210 Szczecin, atariov@zut.edu.pl
Bibliografia
  • [1] Kantor I. and Solodovnikov A., Hypercomplex numbers, Springer-Verlag, New York, 1989.
  • [2] Alfsmann D., Göckler H. G., Sangwine S. J. and Ell T. A., Hypercomplex Algebras in Digital Signal Processing: Benefits and Draw-backs (Tutorial). Proc. EURASIP 15th European Signal Processing Conference (EUSIPCO 2007), Poznań, Poland, (2007), 1322-1326.
  • [3] Alfsmann D., On families of 2N-dimensional hypercomplex algebras suitable for digital signal processing, in Proc. European Signal Processing Conf. (EUSIPCO 2006), Florence, Italy, (2006), 1322-1326.
  • [4] D. J. Alfsmann and H. G. Göckler. Dual Number Subalgebras mapped to Digital Signal Processing Structures. Proc. Eighth International Conference on Mathematics in Signal Processing, The Royal Agricultural College, Cirencester, UK, 16-18 December (2008), 129-132
  • [5] Bülow T. and Sommer G., Hypercomplex signals - a novel extension of the analytic signal to the multidimensional case, IEEE Trans. Sign. Proc., vol. SP-49, nov. (2001), no. 11, 2844– 2852,
  • [6] Witten B. and Shragge J., Quaternion-based Signal Processing. Proceedings of the New Orleans 2006 Annual Meeting, 2862-2865.
  • [7] Sangwine S. J., Le Bihan N., Hypercomplex analytic signals: extension of the analytic signal concept to complex signals, Proc. EURASIP 15th European Signal Processing Conference (EUSIPCO 2007), Poznań, Poland, (2007), 621- 624.
  • [8] Sangwine S. J., Colour image edge detector based on quaternion convolution, Electron. Lett., vol. 34, May (1998), no. 10, 969–971.
  • [9] Sangwine S., Fourier transforms of color images using quaternion or hypercomplex, numbers, Electronics Letters, vol. 32(21), Oct. (1996), 10, 1979–1980.
  • [10] Bayro-Corrochano Eduardo, Multi-resolution image analysis using the quaternion wavelet transform, Numerical Algorithms, Volume 39, (2005), Numbers 1-3, July, 35–55.
  • [11] Bayro-Corrochano Eduardo, The Theory and Use of the Quaternion Wavelet Transform, Journal of Mathematical Imaging and Vision, Volume 24, (2006), Issue 1, 19– 35.
  • [12] Moxey C. E., Sangwine S. J., and Ell T. A., Hypercomplex correlation techniques for vector images, IEEE Trans. Signal Processing, vol. 51, July (2003), 1941–1953.
  • [13] De Groote H.F., On the complexity of quaternion multiplication, Infor. Process. Lett. vol. 43, (1975), no.6, 161- 164.
  • [14] Ell T., Quaternion-Fourier transforms for analysis of twodimensional linear time-invariant partial differential systems, Proceedings of the 32nd IEEE Conference on Decision and Control, 15-17 Dec. (1993), 1830–1841.
  • [15] Ueda K. and Takahashi S. I., Digital filters with hypercomplex coefficients, Proc. IEEE Int. Symp. Circuits Syst., vol. 1, May (1993), 479–482.
  • [16] Dimitrov V.S., Cooklev T.V. and Donevsky B.D., On the multiplication of reduced biquaternions and applications, Infor. Process. Letters, vol. 43, (1992), no 3, 161-164.
  • [17] Hitzer E., Foundations of Multidimensional Wavelet Theory: The Quaternion Fourier Transform and its Generalizations, Preprints of Meeting of the Japan Society for Industrial and Applied Mathematics, Tsukuba University, 16–18 Sep. (2006), Tsukuba, Japan, 66,67.
  • [18] Toyoshima H., Computationally efficient implementation of hypercomplex digital filters, Proc. IEEE Int. Conference on Acoustics, Speech, and Signal Processing (ICASSP ’98), Seattle, USA, vol. 3, (1998), 1761–1764.
  • [19] Pei Soo-Chang, Ding Jian- Jiun, and Chang Ja-Han, Efficient Implementation of Quaternion Fourier Transform, Convolution, and Correlation by 2-D Complex FFT. IEEE Transactions on Signal Processing, vol. 49, (2001), no. 11, 2783-2797.
  • [20] Makarov О. М. An algorithm for the multiplication of two quaternion. Computational Mathematics and Mathematical Physics., т. 17, (1977), no. 6, 1574 –1575. (in Russian).
  • [21] Rososzek S.K., Litwin A.I., Chernyaeva N.E., Fast algorithm of two hypercomplex numbers product. Announcer of the Tomsk State University „Mathematics, Cybernetics, Informatics”, (2000), Nr 269, 66-68. (in Russian).
  • [22] Schütte H.-D. and Wenzel J., Hypercomplex numbers in digital signal processing, Proc. ISCAS’90, New Orleans, (1990), 1557–1560.
  • [23] Ţariov A., Strategie racjonalizacji obliczeń przy wyznaczaniu iloczynów macierzowo-wektorowych. Metody Informatyki stosowanej, (2008), Nr 1, 147- 158.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPOB-0037-0005
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