Abstract
Consideration was given to a new representation of the Meixner filters which, in distinction to the previously proposed filters, have a rational form of representation of any integer values of the additional parameter α, can be used to describe the dynamic systems with fractional order for the noninteger α, and are obtained directly from the continuous generalized Laguerre filters through a modified bilinear transformation. The paper described a design of the proposed nonorthogonal Meixner filter, numerically stable algorithm to optimize the filter parameters, as well as the results of computer experiments corroborating efficiency of the nonorthogonal Meixner filters for solution of practical problems.
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King, R.E. and Paraskevopoulos, P.N., Digital Laguerre Filters Int. J. Circuit Theory Appl., 1977, vol. 5, no. 1, pp. 81–91.
Nurges, Yu., Laguerre Models in the Problems of Approximation and Identification, Autom. Remote Control, 1987, no. 3, pp. 88–96.
Telescu, M., Iassamen, N., Cloastre, P., and Tanguy, N., A Simple Algorithm for Stable Order Reduction of z-domain, Signal Proc., 2013, vol. 93, pp. 332–337.
Nurges, U.A., Meixner Models of Linear Discrete Systems, Autom. Remote Control, 1988, vol. 49, no. 12, pp. 1638–1644.
Meixner, J., Orthogonale Polynomsysteme mit einer besonderen Gestalt der erzeugenden Funktion, J. Lond. Math. Soc., 1934, vol. 9, no. 1, pp. 6–13.
Perov, V.P., Design of Sampled-data Systems in an Orthogonal Basis. III, Autom. Remote Control, 1976, vol. 37, no. 10, pp. 1517–1522.
den Brinker, A.C., Meixner-like Functions Having a Rational z-transform, Int. J. Circuit Theory Appl., 1995, vol. 23, no. 1, pp. 237–246.
Asyali, M.H. and Juusola, M., Use of Meixner Functions in Estimation of Volterra Kernels of Nonlinear Systems with Delay, IEEE Trans. Biomed. Engineer., 2005, vol. 52, no. 2, pp. 229–237.
Oliveira, F.M., Tran, W.H., Lesser, D., et al., Autonomic and Metabolic Effects of OSA in Childhood Obesity, in Proc. 32 Ann. Int. Conf. IEEE EMBS, Buenos Aires, Argentina, 2010, pp. 6134–6137.
Chen, Yi. and Hunter, I.W., Nonlinear Stochastic System Identification of Skin Using Volterra Kernels, Ann. Biomed. Eng., 2013, vol. 41, no. 4, pp. 847–862.
Apartsin, A.S. and Sidler, I.V., Using the Nonclassical Volterra Equations of the First Kind to Model the Developing Systems, Autom. Remote Control, 2013, vol. 74, no. 6, pp. 899–910.
Markova, E.V. and Sidorov, D.N., On One Integral Volterra Model of Developing Dynamical Systems, Autom. Remote Control, 2014, vol. 75, no. 3, pp. 413–421.
Prokhorov, S.A. and Kulikovskikh, I.M., Unique Condition for Generalized Laguerre Functions to Solve Pole Position Problem, Signal Proc., 2015, vol. 108, no. 1, pp. 25–29.
Prokhorov, S.A. and Kulikovskikh, I.M., Condition for Optimality of the Meixner Filters, Zh. Radioelektron.: Electronic Journal, 2015, no. 4. https://doi.org/jre.cplire.ru/mac/apr15/9/text.html
Prokhorov, S.A. and Kulikovskikh, I.M., Pole Position for Meixner Filters, Signal Proc., 2016, vol. 120, no. 1, pp. 8–12.
Klink, W.H. and Payne, G.L., Approximating with Nonorthogonal Basis Functions, J. Comput. Physics, 1976, vol. 21, no. 2, pp. 208–226.
Butkovskii, A.G., Postnov, S.S., and Postnova, E.A., Fractional Integro-Differential Calculus and Its Control-Theoretical Applications. II, Autom. Remote Control, 2013, vol. 74, no. 5, pp. 725–749.
Aoun, M., Malti, R., Levron, F., and Oustaloup, A., Synthesis of Fractional Laguerre Basis for System Approximation, Automatica, 2007, vol. 43, no. 9, pp. 1640–1648.
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Original Russian Text © I.M. Kulikovskikh, 2018, published in Avtomatika i Telemekhanika, 2018, No. 8, pp. 111–128.
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Kulikovskikh, I.M. Meixner Nonorthogonal Filters. Autom Remote Control 79, 1458–1473 (2018). https://doi.org/10.1134/S0005117918080088
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DOI: https://doi.org/10.1134/S0005117918080088