The Current Spectrum Formation of a Non-Periodic Signal: A Differential Approach
The paper deals with the problem of forming spectra of non-periodic signals in real-time. The disadvantage of the existing approaches is the dependence of the formed spectrum on time as a parameter and the possibility of obtaining the signal spectrum in its original definition only for a fixed time,...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-04-01
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| Series: | Inventions |
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| Online Access: | https://www.mdpi.com/2411-5134/5/2/15 |
| _version_ | 1797571356443803648 |
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| author | Sergey Sokolov Daniil Marshakov Arthur Novikov |
| author_facet | Sergey Sokolov Daniil Marshakov Arthur Novikov |
| author_sort | Sergey Sokolov |
| collection | DOAJ |
| description | The paper deals with the problem of forming spectra of non-periodic signals in real-time. The disadvantage of the existing approaches is the dependence of the formed spectrum on time as a parameter and the possibility of obtaining the signal spectrum in its original definition only for a fixed time, as well as a high amount of computation. In this regard, a computationally efficient algorithm is proposed for forming a spectrum of non-periodic functions on a time interval that is constantly updated with a given sampling step, which ensures the invariance of the generated spectrum to time as a parameter. The algorithm is based on obtaining differential equations that are based on generalized differentiation with respect to a variable time interval of spectral components and their solving while using the fourth-order Runge–Kutta method. A numerical simulation of the developed algorithm was performed using the MATLAB mathematical modeling package using the example of a substantially non-linear function. Based on the practical results, a comparative evaluation of computational and time complexity has been performed in solving the problem. Based on the obtained experimental results, it is concluded that it is possible to effectively use the proposed algorithm to calculate the current spectrum of non-periodic functions with the requirement of small sampling steps, i.e., when calculating the spectrum in real-time. |
| first_indexed | 2024-03-10T20:39:15Z |
| format | Article |
| id | doaj.art-da038a0574f244178df5e3b43150f846 |
| institution | Directory Open Access Journal |
| issn | 2411-5134 |
| language | English |
| last_indexed | 2024-03-10T20:39:15Z |
| publishDate | 2020-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Inventions |
| spelling | doaj.art-da038a0574f244178df5e3b43150f8462023-11-19T20:51:16ZengMDPI AGInventions2411-51342020-04-01521510.3390/inventions5020015The Current Spectrum Formation of a Non-Periodic Signal: A Differential ApproachSergey Sokolov0Daniil Marshakov1Arthur Novikov2Computer Technologies and Information Security Faculty, Rostov State University of Economics, 69, Bolshaya Sadovaya, 344002 Rostov-on-Don, RussiaComputer Systems and Information Security Department, Don State TechFigurnical University, 1, Gagarin square, 344000 Rostov-on-Don, RussiaAutomotive Faculty, Voronezh State University of Forestry and Technologies named after G.F. Morozov, 8, Timiryazeva, 394087 Voronezh, RussiaThe paper deals with the problem of forming spectra of non-periodic signals in real-time. The disadvantage of the existing approaches is the dependence of the formed spectrum on time as a parameter and the possibility of obtaining the signal spectrum in its original definition only for a fixed time, as well as a high amount of computation. In this regard, a computationally efficient algorithm is proposed for forming a spectrum of non-periodic functions on a time interval that is constantly updated with a given sampling step, which ensures the invariance of the generated spectrum to time as a parameter. The algorithm is based on obtaining differential equations that are based on generalized differentiation with respect to a variable time interval of spectral components and their solving while using the fourth-order Runge–Kutta method. A numerical simulation of the developed algorithm was performed using the MATLAB mathematical modeling package using the example of a substantially non-linear function. Based on the practical results, a comparative evaluation of computational and time complexity has been performed in solving the problem. Based on the obtained experimental results, it is concluded that it is possible to effectively use the proposed algorithm to calculate the current spectrum of non-periodic functions with the requirement of small sampling steps, i.e., when calculating the spectrum in real-time.https://www.mdpi.com/2411-5134/5/2/15current time intervaldifferential equationsgeneralized differentiationRunge–Kutta methodspectrum of non-periodic functionsspectrum generation algorithm |
| spellingShingle | Sergey Sokolov Daniil Marshakov Arthur Novikov The Current Spectrum Formation of a Non-Periodic Signal: A Differential Approach Inventions current time interval differential equations generalized differentiation Runge–Kutta method spectrum of non-periodic functions spectrum generation algorithm |
| title | The Current Spectrum Formation of a Non-Periodic Signal: A Differential Approach |
| title_full | The Current Spectrum Formation of a Non-Periodic Signal: A Differential Approach |
| title_fullStr | The Current Spectrum Formation of a Non-Periodic Signal: A Differential Approach |
| title_full_unstemmed | The Current Spectrum Formation of a Non-Periodic Signal: A Differential Approach |
| title_short | The Current Spectrum Formation of a Non-Periodic Signal: A Differential Approach |
| title_sort | current spectrum formation of a non periodic signal a differential approach |
| topic | current time interval differential equations generalized differentiation Runge–Kutta method spectrum of non-periodic functions spectrum generation algorithm |
| url | https://www.mdpi.com/2411-5134/5/2/15 |
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