Abstract
The outputs of linear shift-invariant systems are usually defined in terms of the convolution of input signals with the impulse response functions characterizing the systems. In many areas, as for instance, electrical engineering, digital signal and image processing, statistics, physic, optics, etc., convolution systems defined on finite groups are used. Such systems can be modeled and represented by convolution matrices. The problem is that due to the complexity of systems, dealing with large matrices is required. In this paper, we discuss representation of convolution systems on finite groups by Heterogeneous decision diagrams (HDDs). Such representations permit compact representations of convolution systems, and thanks to that, efficient manipulations and computations related to investigation of features and applications of such systems.
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References
Clarke, E.M., Fujita, M., Zhao, X.: Multi-terminal binary decision diagrams and hybrid decision diagrams. In: Sasao, T., Fujita, M. (eds.) Representations of Discrete Functions, pp. 93–108. Kluwer Academic Publishers, Dordrecht (1996)
Endow, Y.: Walsh harmonizable processes in linear system theory. Cybernetics and Systems, 489–512 (1996)
Gibbs, J.E., Stanković, R.S.: Why IWGD-89? a look at the bibliography of Gibbs derivatives. In: Butzer, P.L., Stanković, R.S. (eds.) Theory and Applications of Gibbs Derivatives, Belgrade, Serbia, Matematički Institut, pp. xi–xxiv (1990)
Karpovsky, M.G., Trachtenberg, E.A.: Some optimization problems for convolution systems over finite groups. Inf. and Control 34, 227–247 (1977)
Miller, D.M., Stanković, R.S.: A heterogeneous decision diagram package. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds.) EUROCAST 2009. LNCS, vol. 5717, pp. 540–547. Springer, Heidelberg (2009)
Miller, D., Thornton, M.: QMDD: A decision diagram structure for reversible and quantum circuits. In: Proc. Int. Symp. on Multiple-Valued Logic, CD, p. 6 (2006)
Moraga, C.: Introduction to linear p-adic systems. In: Trappl, R. (ed.) Cybernetics and Systems Research, vol. 2. North-Holland, Amsterdam (1984)
Pearl, J.: Optimal dyadic models of time-invariant systems. IEEE Trans. Computers C-24 (1975)
Pichler, F.R.: Some aspects of a theory of correlation with respect to Walsh harmonic analysis. Univ. Maryland Tech. Res. Rept R-70-11 (1970)
Pichler, F.: On state space description of linear dyadic invariant systems. IEEE Trans. on Electromagnetic Compatibility EMC-13, 166 (1971)
Pichler, F.R.: Dyadische Faltungsoperatoren zur Beschreibung linearer Systeme. Siteber. Öst. Akad. Wiss., Math.-naturwiss. KL, Abt. II 180, Heft 1-3, 69–87 (1971)
Pichler, F.: Construction of dissipative dynamical system using Gibbs derivatives. In: Stanković, R.S. (ed.) Walsh and Dyadic Analysis, Elektronski fakultet, Niš, Serbia, pp. 31–36 (2008); ISBN 978-86-85195-47-1
Stanković, S., Astola, J.: XML Framework for various types of decision diagrams for discrete functions. IEICE - Transactions on Information and Systems E90-D(11), 1731–1740 (2007)
Stanković, S., Astola, J.T., Miller, D.M., Stanković, R.S.: Heterogeneous decision diagrams for applications in Harmonic Analysis on finite non-Abelian groups. In: Proc. 40th Int. Symp. on Multiple-Valued Logic, Barcelona, Spain, May 26-18, pp. 307–312. IEEE-CS-Press, Los Alamitos (2010)
Stanković, R.S., Stanković, M.S., Moraga, C.: Remarks on systems and differential operators on groups. Facta Universitatis (Niš), Ser. Elec. Energ. 18(3), 531–545 (2005)
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Stanković, S., Stanković, R.S., Astola, J.T., Moraga, C. (2012). Representation of Convolution Systems on Finite Groups by Heterogeneous Decision Diagrams. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2011. EUROCAST 2011. Lecture Notes in Computer Science, vol 6928. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27579-1_38
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DOI: https://doi.org/10.1007/978-3-642-27579-1_38
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