Improving the Accuracy of the Pencil of Function Method Increasing Its Matrix Polynomial Degree
The estimation of complex natural frequencies in linear systems through their transient response analysis is a common practice in engineering and applied physics. In this context, the conventional Generalized Pencil of Function (GPOF) method that employs a matrix pencil of degree one, utilizing sing...
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MDPI AG
2025-01-01
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| author | Raul H. Barroso Alfonso J. Zozaya Sahad |
| author_facet | Raul H. Barroso Alfonso J. Zozaya Sahad |
| author_sort | Raul H. Barroso |
| collection | DOAJ |
| description | The estimation of complex natural frequencies in linear systems through their transient response analysis is a common practice in engineering and applied physics. In this context, the conventional Generalized Pencil of Function (GPOF) method that employs a matrix pencil of degree one, utilizing singular value decomposition (SVD) filtering, has emerged as a prominent strategy to carry out a complex natural frequency estimation. However, some modern engineering applications increasingly demand higher accuracy estimation. In this context, some intrinsic properties of Hankel matrices and exponential functions are utilized in this paper in order to develop a modified GPOF method which employs a matrix pencil of degree greater than one. Under conditions of low noise in the transient response, our method significantly enhances accuracy compared to the conventional GPOF approach. This improvement is especially valuable for applications involving closely spaced complex natural frequencies, where a precise estimation is crucial. |
| format | Article |
| id | doaj-art-eec0e5bcc6d740f3b48c799d148d2ebf |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj-art-eec0e5bcc6d740f3b48c799d148d2ebf2025-01-24T13:40:09ZengMDPI AGMathematics2227-73902025-01-0113231510.3390/math13020315Improving the Accuracy of the Pencil of Function Method Increasing Its Matrix Polynomial DegreeRaul H. Barroso0Alfonso J. Zozaya Sahad1Departamento de Electrónica y Circuitos, Universidad Simon Bolívar, Caracas, Miranda, VenezuelaDepartamento de Electricidad, Facultad de Ingeniería, Universidad Tecnológica Metropolitana, Santiago, ChileThe estimation of complex natural frequencies in linear systems through their transient response analysis is a common practice in engineering and applied physics. In this context, the conventional Generalized Pencil of Function (GPOF) method that employs a matrix pencil of degree one, utilizing singular value decomposition (SVD) filtering, has emerged as a prominent strategy to carry out a complex natural frequency estimation. However, some modern engineering applications increasingly demand higher accuracy estimation. In this context, some intrinsic properties of Hankel matrices and exponential functions are utilized in this paper in order to develop a modified GPOF method which employs a matrix pencil of degree greater than one. Under conditions of low noise in the transient response, our method significantly enhances accuracy compared to the conventional GPOF approach. This improvement is especially valuable for applications involving closely spaced complex natural frequencies, where a precise estimation is crucial.https://www.mdpi.com/2227-7390/13/2/315pencilPronyresonancesuper-resolutionaccuracypolynomial matrix |
| spellingShingle | Raul H. Barroso Alfonso J. Zozaya Sahad Improving the Accuracy of the Pencil of Function Method Increasing Its Matrix Polynomial Degree Mathematics pencil Prony resonance super-resolution accuracy polynomial matrix |
| title | Improving the Accuracy of the Pencil of Function Method Increasing Its Matrix Polynomial Degree |
| title_full | Improving the Accuracy of the Pencil of Function Method Increasing Its Matrix Polynomial Degree |
| title_fullStr | Improving the Accuracy of the Pencil of Function Method Increasing Its Matrix Polynomial Degree |
| title_full_unstemmed | Improving the Accuracy of the Pencil of Function Method Increasing Its Matrix Polynomial Degree |
| title_short | Improving the Accuracy of the Pencil of Function Method Increasing Its Matrix Polynomial Degree |
| title_sort | improving the accuracy of the pencil of function method increasing its matrix polynomial degree |
| topic | pencil Prony resonance super-resolution accuracy polynomial matrix |
| url | https://www.mdpi.com/2227-7390/13/2/315 |
| work_keys_str_mv | AT raulhbarroso improvingtheaccuracyofthepenciloffunctionmethodincreasingitsmatrixpolynomialdegree AT alfonsojzozayasahad improvingtheaccuracyofthepenciloffunctionmethodincreasingitsmatrixpolynomialdegree |