The Mathematical Model of Cyclic Signals in Dynamic Systems as a Cyclically Correlated Random Process
This work is devoted to the procedure for constructing of a cyclically correlated random process of a continuous argument as a mathematical model of cyclic signals in dynamic systems, which makes it possible to consistently describe cyclic stochastic signals, both with regular and irregular rhythms,...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/18/3406 |
| _version_ | 1797485175138942976 |
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| author | Serhii Lupenko |
| author_facet | Serhii Lupenko |
| author_sort | Serhii Lupenko |
| collection | DOAJ |
| description | This work is devoted to the procedure for constructing of a cyclically correlated random process of a continuous argument as a mathematical model of cyclic signals in dynamic systems, which makes it possible to consistently describe cyclic stochastic signals, both with regular and irregular rhythms, not separating them, but complementing them within the framework of a single integrated model. The class of cyclically correlated random processes includes the subclass of cyclostationary (periodically) correlated random processes, which enable the use of a set of powerful methods of analysis and the forecasting of cyclic signals with a stable rhythm. Mathematical structures that model the cyclic, phase and rhythmic structures of a cyclically correlated random process are presented. The sufficient and necessary conditions that the structural function and the rhythm function of the cyclically correlated random process must satisfy have been established. The advantages of the cyclically correlated random process in comparison with other mathematical models of cyclic signals with a variable rhythm are given. The obtained results contribute to the emergence of a more complete and rigorous theory of this class of random processes and increase the validity of the methods of their analysis and computer simulation. |
| first_indexed | 2024-03-09T23:15:02Z |
| format | Article |
| id | doaj.art-bd309dfb8d6c4e4186f8b0e5770f9bb8 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:15:02Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-bd309dfb8d6c4e4186f8b0e5770f9bb82023-11-23T17:38:14ZengMDPI AGMathematics2227-73902022-09-011018340610.3390/math10183406The Mathematical Model of Cyclic Signals in Dynamic Systems as a Cyclically Correlated Random ProcessSerhii Lupenko0Faculty of Electrical Engineering, Automatic Control and Informatics of Opole University of Technology, 45-758 Opole, PolandThis work is devoted to the procedure for constructing of a cyclically correlated random process of a continuous argument as a mathematical model of cyclic signals in dynamic systems, which makes it possible to consistently describe cyclic stochastic signals, both with regular and irregular rhythms, not separating them, but complementing them within the framework of a single integrated model. The class of cyclically correlated random processes includes the subclass of cyclostationary (periodically) correlated random processes, which enable the use of a set of powerful methods of analysis and the forecasting of cyclic signals with a stable rhythm. Mathematical structures that model the cyclic, phase and rhythmic structures of a cyclically correlated random process are presented. The sufficient and necessary conditions that the structural function and the rhythm function of the cyclically correlated random process must satisfy have been established. The advantages of the cyclically correlated random process in comparison with other mathematical models of cyclic signals with a variable rhythm are given. The obtained results contribute to the emergence of a more complete and rigorous theory of this class of random processes and increase the validity of the methods of their analysis and computer simulation.https://www.mdpi.com/2227-7390/10/18/3406cyclic signalsirregular rhythmdynamic systemscyclically correlated random process |
| spellingShingle | Serhii Lupenko The Mathematical Model of Cyclic Signals in Dynamic Systems as a Cyclically Correlated Random Process Mathematics cyclic signals irregular rhythm dynamic systems cyclically correlated random process |
| title | The Mathematical Model of Cyclic Signals in Dynamic Systems as a Cyclically Correlated Random Process |
| title_full | The Mathematical Model of Cyclic Signals in Dynamic Systems as a Cyclically Correlated Random Process |
| title_fullStr | The Mathematical Model of Cyclic Signals in Dynamic Systems as a Cyclically Correlated Random Process |
| title_full_unstemmed | The Mathematical Model of Cyclic Signals in Dynamic Systems as a Cyclically Correlated Random Process |
| title_short | The Mathematical Model of Cyclic Signals in Dynamic Systems as a Cyclically Correlated Random Process |
| title_sort | mathematical model of cyclic signals in dynamic systems as a cyclically correlated random process |
| topic | cyclic signals irregular rhythm dynamic systems cyclically correlated random process |
| url | https://www.mdpi.com/2227-7390/10/18/3406 |
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