J.A. Kalinovsky, Y.E. Boyarinova , J.V. Khitsko
Èlektron. model. 2019, 41(4):03-17
ABSTRACT
The article presents themethod of selecting hypercomplex number systems (HNS) formodeling digitalThe article presents themethod of selecting hypercomplex number systems (HNS) formodeling digitalreversible filters based on the analysis of the expression of the norm of the hypercomplex transferfunction denominator. The selected HNS, allowing to obtain in the transfer function of the filter acomplete set of powers of the shift operator. These HNS have weakly filled isomorphisms, the transitionto which can significantly reduce the number of real operations in the operation of the filter.
KEYWORDS
hypercomplex number system, linear convolution, isomorphism, multiplication,hypercomplex number system, linear convolution, isomorphism, multiplication,bicomplex numbers, quadriplex numbers, computer algebra system.
REFERENCES
2. Toyoshima, H. (2002), “Computationally Efficient Implementation of Hypercomplex Digital Filters”, Fundamentals, pp. 1870-1876.
3. Schutte, H.D. (1991), Digital filter for processing complex and hypercomplex signals, Paderborn, Germany.
4. Schulz, D., Seitz, J. and LustosadaCosta J.P. (2011), “Widely Linear SIMO Filtering for Hypercomplex Numbers”, IEEE Information Theory Workshop, pp. 390-394.
https://doi.org/10.1109/ITW.2011.6089486
5. Toyoshima, H. and Higuchi, S. (1999), “Design of Hypercomplex All-Pass Filters to Realize Complex Transfer Functions”, Conference proceedings of the second International conference on Information, Communications and Signal Processing, pp. 1-5.
6. Toyoshima, H. (1998), “Computationally Efficient Bicomplex Multipliers for Digital Signal Processing”, Inf. & Syst, pp. 236-238.
7. Bulow, T. and Sommer, G. (2001), “Hypercomplex Signals — A Novel Extension of the Analytic Signal to the Multidimensional Case”, IEEE Transactions on Signal Processing, Vol. 49, no. 11, pp. 2844-2852.
https://doi.org/10.1109/78.960432
8. Parfieniuk, M. and Petrovsky, A. (2004), “Quaternionic building block for paraunitary filter banks”, Proceeding of the 12th European Signal Processing Conference (EUSIPCO '04), Vienna, Austria, 2004, pp. 1237-1240.
9. Alfsmann, D. and Göckler, H. G. (2005), “Design of Hypercomplex Allpass-Based Paraunitary Filter Banks applying Reduced Biquaternions”, Proceeding of EUROCON 2005, Belgrade, Serbia & Montenegro, 2005, pp. 92-95.
https://doi.org/10.1109/EURCON.2005.1629866
10. Ueda, K. and Takahashi, S. (1993) “Digital Filtrs with hypercomplex Coefficients”, ISCAP, pp. 479-482.
11. Kalinovsky, Ya.O. (2007), “Development of methods of the theory of hypercomplex numbers systems for mathematical modeling and computer calculations”, Abstract of Cand. Sci. (Tech.) dissertation, Kyiv, Ukraine.
12. Kalinovsky, Y.A., Boyarinova, Y.E. and Khitsko, Y.V. (2015), “Reversible Digital Filters Total Parametric Sensitivity Optimization using Non-canonical Hypercomplex Number Systems”, available at: http://arxiv.org/abs/1506.01701 (accessed June 23, 2019).
13. Sinkov, Ì.V., Kalinovsky, Ya.A. and Boyarinova, Yu.E. (2010), Konechnomernyie giperkompleksnyie chislovyie sistemy [Finite-dimensional hypercomplex number systems], Infodruk,
Kyiv, Ukraine.
14. Mel'nikov O.V., Remeslennikov V.N. and Roman'kov V.A.(1990), “General algebra”,
Nauka, Vol. 1.
15. Drozd, Yu.A., Kirichenko, V.V. (1980), Konechnomernyye algebry [Finite-dimensional algebras],Vyshcha shkola, Kyiv, Ukraine.
16. Kalinovskiy, Ya.A., Boyarinova, Yu.Ye., Khitsko, Ya.V., Sukalo, A.S. (2017), “Software complexfor hypercomplex computing”, Elektronnoye. modelirovaniye, Vol. 39, no. 5, pp. 81-96.
https://doi.org/10.15407/emodel.39.05.081
Full text: PDF