Meixner Nonorthogonal Filters

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.

Keywords

Meixner filter, optimization of the filter poles, bilinear transformation, delay system

Received

30.09.2018

Publication date

30.09.2018

Number of characters

790

Cite Download pdf To download PDF you should sign in

GOST	Kulikovskikh I. Meixner Nonorthogonal Filters // Avtomatika i Telemekhanika – 2018. – Issue 8 C. 111-128 [Electronic resource]. URL: http://ras.jes.su/ait/s207987840000498-6-1-en (circulation date: 20.04.2024). DOI: 10.31857/S000523100001251-0
MLA	Kulikovskikh, Ilona "Meixner Nonorthogonal Filters." Avtomatika i Telemekhanika 8 (2018):111-128. DOI: 10.31857/S000523100001251-0
APA	Kulikovskikh I. (2018). Meixner Nonorthogonal Filters. Avtomatika i Telemekhanika (8), pp.111-128 DOI: 10.31857/S000523100001251-0

Размещенный ниже текст является ознакомительной версией и может не соответствовать печатной

Readers community rating: votes 0

1. King R.E., Paraskevopoulos P.N. Digital Laguerre Filters // Int. J. Circuit Theory Appl. 1977. V. 5. No. 1. P. 81–91.

2. Nurges Yu. Lagerrovy modeli v zadachakh approksimatsii i identifikatsii // AiT. 1987. № 3. S. 88–96.

3. Telescu M., Iassamen N., Cloastre P., Tanguy N. A Simple Algorithm for Stable Order Reduction of z-domain // Signal Proc. 2013. V. 93. P. 332–337.

4. Nurges U.A. Meixner Models of Linear Discrete Systems // Autom. Remote Control. 1988. V. 49. No. 12. P. 1638–1644.

5. Meixner J. Orthogonale polynomsysteme mit einer besonderen gestalt der erzeugenden funktion // J. Lond. Math. Soc. 1934. V. 9. No. 1. P. 6–13.

6. Perov V.P. Design of Sampled-data Systems in an Orthogonal Basis. III // Autom. Remote Control. 1976. V. 37. No. 10. P. 1517–1522.

7. den Brinker A.C. Meixner-like Functions Having a Rational z-transform // Int. J. Circuit Theory Appl. 1995. V. 23. No. 1. P. 237–246.

8. Asyali M.H., Juusola M. Use of Meixner Functions in Estimation of Volterra Kernels of Nonlinear Systems with Delay // IEEE Trans. Biomed. Engineer. 2005. V. 52. No. 2. P. 229–237.

9. Oliveira F.M., Tran W.H., Lesser D., Bhatia R., Ortega R., Mittelman S.D., Keens T.G., Davidson Ward S.L., Khoo M.C. Autonomic and Metabolic Effects of OSA in Childhood Obesity // Proc. 32 Ann. Int. Conf. IEEE EMBS. Buenos Aires, Argentina, 2010. P. 6134–6137.

10. Chen Yi, Hunter I.W. Nonlinear Stochastic System Identification of Skin Using Volterra Kernels // Ann. Biomed. Eng. 2013. V. 41. No. 4. P. 847–862.

11. Apartsin A.S., Sidler I.V. Using the Nonclassical Volterra Equations of the First Kind to Model the Developing Systems // Autom. Remote Control. 2013. V. 74. No. 6. P. 899–910.

12. Markova E.V., Sidorov D.N. On one Integral Volterra Model of Developing Dynamical Systems // Autom. Remote Control. 2014. V. 75. No. 3. P. 413–421.

13. Prokhorov S.A., Kulikovskikh I.M. Unique Condition for Generalized Laguerre Functions to Solve Pole Position Problem // Signal Proc. 2015. V. 108. No. 1. P. 25–29.

14. Prokhorov S.A., Kulikovskikh I.M. Uslovie optimal'nosti fil'trov Mejksnera // Zhurn. radioehlektroniki: ehlektronnyj zhurnal. 2015. № 4. URL: http://jre.cplire.ru/mac/apr15/9/text.html

15. Prokhorov S.A., Kulikovskikh I.M. Pole Position for Meixner Filters // Signal Proc. 2016. V. 120. No. 1. P. 8–12.

16. Klink W.H., Payne G.L. Approximating with Nonorthogonal Basis Functions // J. Comput. Physics. 1976. V. 21. No. 2. P. 208–226.

17. Butkovskii A.G., Postnov S.S., Postnova E.A. Fractional Integro-Differential Calculus and its Control-Theoretical Applications. II // Autom. Remote Control. 2013. V. 74. No. 5. P. 725–749.

18. Aoun M., Malti R., Levron F., Oustaloup A. Synthesis of Fractional Laguerre Basis for System Approximation // Automatica. 2007. V. 43. No. 9. P. 1640–1648.