Cyclic linear random process as a mathematical model of cyclic signals

Czasopismo : Acta Mechanica et Automatica
Tytuł artykułu : Cyclic linear random process as a mathematical model of cyclic signals

Autorzy :
Bąk, Ł.
Faculty of Mechanical Engineering and Aeronautics, Rzeszow University of Technology, Al. Powstańców Warszawy12, 35-959 Rzeszów, Poland, lbak@prz.edu.pl,
Noga, S.
Faculty of Mechanical Engineering and Aeronautics, Rzeszow University of Technology, Al. Powstańców Warszawy12, 35-959 Rzeszów, Poland, noga@prz.edu.pl,
Stachowicz, F.
Faculty of Mechanical Engineering and Aeronautics, Rzeszow University of Technology, Al. Powstańców Warszawy12, 35-959 Rzeszów, Poland, stafel@prz.edu.pl,
Tesař, V.
Institute of Thermomechanics v.v.i., Academy of Sciences of the Czech Republic, Dolejškova 1402/5, 182 00 Praha 8, Czech Republic, tesar@it.cas.cz,
Czerwiński, E.
Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, ul. Stefanowskiego 1/15, 90-924 Łódź, Poland, ernest.czerwinski@dokt.p.lodz.pl,
Olejnik, P.
Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, ul. Stefanowskiego 1/15, 90-924 Łódź, Poland, pawel.olejnik@p.lodz.pl,
Awrejcewicz, J.
Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, ul. Stefanowskiego 1/15, 90-924 Łódź, Poland, jan.awrejcewicz@p.lodz.pl,
Wudarczyk, S.
Faculty of Mechanical Engineering, Department of Biomedical Engineering, Mechatronics and Theory of Mechanisms, Wroclaw University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland, slawomir.wudarczyk@pwr.edu.pl,
Muraszkowski, A.
Faculty of Mechanical Engineering, Department of Biomedical Engineering, Mechatronics and Theory of Mechanisms, Wroclaw University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland, artur.muraszkowski@pwr.edu.pl,
Lupenko, S.
Ternopil Ivan Pul’uj National Technical University,46001, Ruska str. 56, Ternopil, Ukraine, lupenko@ua.fm,
Lutsyk, N.
Ternopil Ivan Pul’uj National Technical University,46001, Ruska str. 56, Ternopil, Ukraine, lutsyk.nadiia@gmail.com,
Lapusta, Y.
French Institute of Advanced Mechanics, Institut Pascal / UBP / IFMA / CNRS / Clermont Université, BP 265, 63175 Aubière CEDEX, France, yuri.lapusta@ifma.fr,
Abstrakty : In this study the cyclic linear random process is defined, that combines the properties of linear random process and cyclic random process. This expands the possibility describing cyclic signals and processes within the framework of linear random processes theory and generalizes their known mathematical model as a linear periodic random process. The conditions for the kernel are given and the probabilistic characteristics of generated process of linear random process in order to be a cyclic random process. The advantages of the cyclic linear random process are presented. It can be used as the mathematical model of the cyclic stochastic signals and processes in various fields of science and technology.

Słowa kluczowe : proces cykliczny, model matematyczny, sygnał okresowy, linear cyclic random process, mathematical model, rhythm function, factorized kernel,
Wydawnictwo : Oficyna Wydawnicza Politechniki Białostockiej
Rocznik : 2015
Numer : Vol. 9, no. 4
Strony : 219 – 224
Bibliografia : 1. Yurekli K., Kurunc A., Ozturk F., (2005) Application of linear stochastic models to monthly flow data of Kelkit Stream, Ecological Modelling, 183 (1), 67–75.
2. Blake I., Thomas J. (1968), The Linear Random Process, Proc. Of IEEE, 56 (10) 1696–1703.
3. Bartlett M. (1955), An introduction to stochastic processes with special reference to methods and applications, Cambridge University Press.
4. Medvegyev P. (2007), Stochastic Integration Theory, Oxford University Press, New York.
5. Bhansali R. (1993), Estimation of the impulse response coefficients of a linear process with infinite variance, Journal of Multivariate Analysis, 45, 274-290.
6. Giraitis L. (1985), Central limit theorem for functionals of a linear process, Lithuanian Mathematical Journal, 25, 25–35.
7. Olanrewaju J., Al-Arfaj M. (2005), Development and application of linear process model in estimation and control of reactive distillation, Computers and Chemical Engineering, 30, 147–157.
8. Bartlett M. (1950) Periodogram Analysis and Continuous Spectra, Biometrika, 37(1/2), 1–16.
9. Martchenko B. (1998) Concerning on a theorem for periodic in Slutskiy sense linear random processes, International Congress of Mathematicians, Berlin.
10. Zvarich V., Marchenko B. (2011), Linear autoregressive processes with periodic structures as models of information signals, Radioelectronics and Communications Systems, 54(7), 367–372.
11. Pagano M. (1978), On periodic and multiple autoregressions, The Annals of Statistics, 6, 1310–1317.
12. Lupenko S. (2006), Deterministic and random cyclic function as a model of oscillatory phenomena and signals: the definition and classification, Electronic Modeling, Institute of modeling problems in power of H.E Pukhov NAS, 28, 29–45.
13. Naseri H., Homaeinezhad M.R., Pourkhajeh H., (2013), Noise/spike detection in phonocardiogram signal as a cyclic random process with non-stationary period interval, Computers in Biology and Medicine, 43, 1205–1213.
14. Berkes I., Horváth L., (2006), Convergence of integral functionals of stochastic processes, Econometric Theory, 22, 304–322.
15. Protter P.E., (2005), Stochastic integration and differential equations, Second edition, New York.
16. Gardner W., Napolitano A., Paura L., (2006) Cyclostationarity: Half a century of research, Signal Processing, 86, 639–697.
17. Hurd H., Miamee A. (2006), Periodically Correlated Random Sequences, Spectral Theory and Practice, Wiley, New York.
DOI :
Cytuj : Bąk, Ł. ,Noga, S. ,Stachowicz, F. ,Tesař, V. ,Czerwiński, E. ,Olejnik, P. ,Awrejcewicz, J. ,Wudarczyk, S. ,Muraszkowski, A. ,Lupenko, S. ,Lutsyk, N. ,Lapusta, Y. , Cyclic linear random process as a mathematical model of cyclic signals. Acta Mechanica et Automatica Vol. 9, no. 4/2015
facebook