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Articles

Analytical solution of optimal Meixner-like pole

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Pages 84-96 | Received 02 Jan 2018, Accepted 08 Dec 2018, Published online: 08 Jan 2019

References

  • P. Beckmann, Orthogonal Polynomials for Engineers and Physicists, Golem, Boulder, CO, 1973.
  • H.J.W. Belt and A.C. den Brinker, Optimal parametrization of truncated generalized Laguerre series, Proceedings of ICASSP International Conference on Acoustics, Speech and Signal Processing, Munich, Germany, 21–24 Apr. 1997, pp. 3805–3808.
  • K. Bouzrara, T. Garna, J. Ragot and H. Messaoud, Online identification of the ARX model expansion on Laguerre orthonormal bases with filters on model input and output, Int. J. Control 86(3) (2013), pp. 369–385. doi: 10.1080/00207179.2012.732710
  • P.W. Broome, Discrete orthonormal sequences, J. ACM 12 (1965), pp. 151–168. doi: 10.1145/321264.321265
  • A.C. Den Brinker, Meixner-like functions having a rational Z-transform, Int. J. Circuits Theory Appl. 23 (1995), pp. 237–246. doi: 10.1002/cta.4490230306
  • A.C. Den Brinker and H.J.W. Belt, Optimal free parameters in orthonormal approximations, IEEE Trans. Signal Process. 46(8) (1998). doi: 10.1109/78.705414
  • A.C. Den Brinker, F.P.A. Benders, T.O.e. Silva, Optimality conditions for truncated Kautz series, IEEE Trans. Circuits Syst. 11(43) (1996), pp. 117–122. doi: 10.1109/82.486458
  • Y. Fu and G.A. Dumont, An optimum time scale for discrete Laguerre network, IEEE Trans. Autom. Control 38 (1993), pp. 934–938. doi: 10.1109/9.222305
  • M.J. Gottlieb, Concerning some polynomials orthogonal on a finite or enumerable set of points, Am. J. Math. 60 (1938), pp. 453–458. doi: 10.2307/2371307
  • A. Krifa and K. Bouzrara, Parametric complexity reduction of discrete-time linear systems having a slow initial onset or delay, Math. Model. Anal. 21(5) (2016), pp. 668–684. doi: 10.3846/13926292.2016.1208119
  • L. Leyra Fontaina, Relations between moments in the time and transform domain, Research Report, Vol. 97-E-306, Eindhoven University of Technology, Eindhoven, The Netherlands, 1997.
  • S. Maraoui, A. Krifa and K. Bouzrara, Model reduction of discrete-time linear systems using Meixner-like filters, IMA J. Math. Control Inf. (2016).
  • S. Maraoui, A. Krifa and K. Bouzrara, System approximations based on Meixner-like models, IET Signal Process. 10(5) (2016), pp. 457–464. doi: 10.1049/iet-spr.2015.0091
  • A. Mbarek, K. Bouzrara, T. Garna, J. Ragot, Jos and H. Messaoud, Laguerre-based modelling and predictive control of multi-input multi-output systems applied to a communicating two-tank system (CTTS), Trans. Inst. Meas. Control (2015).
  • L.S.H. Ngia, Separable nonlinear least-squares methods for efficient off-line and on-line modeling of systems using Kautz and Laguerre filters, IEEE Trans. Circuits Syst. II 48(6) (2001), pp. 562–579. doi: 10.1109/82.943327
  • A.F. Nikiforov, S.K. Suslov and V.B. Uvarov, Classical Orthogonal Polynomials of a Discrete Variable, Springer-Verlag, Berlin, Heidelberg, 1991. Springer Series in Computational Physics.
  • T.W. Parks, Choice of time scale in Laguerre approximations using signal measurements, IEEE Trans. Autom. Control AC-16 (1971), pp. 511–513. doi: 10.1109/TAC.1971.1099780
  • S.A. Prokhorov and I.M. Kulikovskikh, Unique condition for generalized Laguerre functions to solve pole position problem, Signal Process. 108 (2015), pp. 25–29. doi: 10.1016/j.sigpro.2014.08.040
  • S.A. Prokhorov and I.M. Kulikovskikh, Pole position problem for Meixner filters, Signal Process. 120 (2016), pp. 8–12. doi: 10.1016/j.sigpro.2015.08.009
  • T.O.e. Silva, Optimality conditions for truncated Laguerre networks, IEEE Trans. Signal Process. 42(9) (1994), pp. 2528–2530. doi: 10.1109/78.317879
  • T.O.e. Silva and H.J.W. Belt, On the determination of the optimal center and scale factor for truncated Hermite series, Signal Processing VIII: Theories and Applications, Proceedings of EUSIPCO, Eighth European Signal Processing Conference, Trieste, Italy, 10–13 Sept. 1996, pp. 1563–1566.
  • N. Tanguy, R. Morvan, P. Vilbe and L.C. Calvez, Pertinent choice of parameters for discrete Kautz approximation, IEEE Trans. Autom. Control 47(5) (2002), pp. 783–787. doi: 10.1109/TAC.2002.1000273
  • N. Tanguy, P. Vilbe and L.C. Calvez, Optimum choice of free parameter in orthonormal approximations, IEEE Trans. Autom. Control 40 (1995), pp. 1811–1813. doi: 10.1109/9.467666

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