Numerical Inverse Transformation Methods for Z-Transform
Numerical inverse Z-transformation (NIZT) methods have been efficiently used in engineering practice for a long time. In this paper, we compare the abilities of the most widely used NIZT methods, and propose a new variant of a classic NIZT method based on contour integral approximation, which is eff...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/4/556 |
| _version_ | 1797570998932865024 |
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| author | Illés Horváth András Mészáros Miklós Telek |
| author_facet | Illés Horváth András Mészáros Miklós Telek |
| author_sort | Illés Horváth |
| collection | DOAJ |
| description | Numerical inverse Z-transformation (NIZT) methods have been efficiently used in engineering practice for a long time. In this paper, we compare the abilities of the most widely used NIZT methods, and propose a new variant of a classic NIZT method based on contour integral approximation, which is efficient when the point of interest (at which the value of the function is needed) is smaller than the order of the NIZT method. We also introduce a vastly different NIZT method based on concentrated matrix geometric (CMG) distributions that tackles the limitations of many of the classic methods when the point of interest is larger than the order of the NIZT method. |
| first_indexed | 2024-03-10T20:33:22Z |
| format | Article |
| id | doaj.art-cc8c7fa020364712a8e035ece74ae698 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T20:33:22Z |
| publishDate | 2020-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-cc8c7fa020364712a8e035ece74ae6982023-11-19T21:15:10ZengMDPI AGMathematics2227-73902020-04-018455610.3390/math8040556Numerical Inverse Transformation Methods for Z-TransformIllés Horváth0András Mészáros1Miklós Telek2MTA-BME Information Systems Research Group, 1117 Budapest, HungaryDepartment of Networked Systems and Services, Technical University of Budapest, 1117 Budapest, HungaryDepartment of Networked Systems and Services, Technical University of Budapest, 1117 Budapest, HungaryNumerical inverse Z-transformation (NIZT) methods have been efficiently used in engineering practice for a long time. In this paper, we compare the abilities of the most widely used NIZT methods, and propose a new variant of a classic NIZT method based on contour integral approximation, which is efficient when the point of interest (at which the value of the function is needed) is smaller than the order of the NIZT method. We also introduce a vastly different NIZT method based on concentrated matrix geometric (CMG) distributions that tackles the limitations of many of the classic methods when the point of interest is larger than the order of the NIZT method.https://www.mdpi.com/2227-7390/8/4/556inverse Z-transformationnumerical analysiscontour integralfinite order approximationmatrix geometric distribution |
| spellingShingle | Illés Horváth András Mészáros Miklós Telek Numerical Inverse Transformation Methods for Z-Transform Mathematics inverse Z-transformation numerical analysis contour integral finite order approximation matrix geometric distribution |
| title | Numerical Inverse Transformation Methods for Z-Transform |
| title_full | Numerical Inverse Transformation Methods for Z-Transform |
| title_fullStr | Numerical Inverse Transformation Methods for Z-Transform |
| title_full_unstemmed | Numerical Inverse Transformation Methods for Z-Transform |
| title_short | Numerical Inverse Transformation Methods for Z-Transform |
| title_sort | numerical inverse transformation methods for z transform |
| topic | inverse Z-transformation numerical analysis contour integral finite order approximation matrix geometric distribution |
| url | https://www.mdpi.com/2227-7390/8/4/556 |
| work_keys_str_mv | AT illeshorvath numericalinversetransformationmethodsforztransform AT andrasmeszaros numericalinversetransformationmethodsforztransform AT miklostelek numericalinversetransformationmethodsforztransform |