Period and signal reconstruction from the curve of trains of samples
Abstract A finite sequence of equidistant samples (a sample‐train) of a periodic signal can be identified with a point in a multidimensional space. Such a point depends on the signal, the sampling period, and the starting time of the sequence. If the starting time varies, then the corresponding poin...
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| Format: | Article |
| Language: | English |
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Wiley
2022-04-01
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| Series: | IET Signal Processing |
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| Online Access: | https://doi.org/10.1049/sil2.12086 |
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| _version_ | 1849306195119046656 |
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| author | Marek W. Rupniewski |
| author_facet | Marek W. Rupniewski |
| author_sort | Marek W. Rupniewski |
| collection | DOAJ |
| description | Abstract A finite sequence of equidistant samples (a sample‐train) of a periodic signal can be identified with a point in a multidimensional space. Such a point depends on the signal, the sampling period, and the starting time of the sequence. If the starting time varies, then the corresponding point moves along a closed curve. We prove that this curve, that is, the set of all sample‐trains of a given length, determines the signal period, provided that the sampling period is known and is smaller than half of the signal period. The presented result is proved with the help of the theory of rotation numbers developed by Poincaré. We also prove that the curve of sample‐trains determines the signal up to a time shift, provided that the ratio of the sampling period to the period of the signal is irrational. A counterexample shows that the assumption on the incommensurability of the periods cannot be dropped. Eventually, we show how to estimate the period of a signal from a finite number of its sample‐trains. |
| format | Article |
| id | doaj-art-38e5f028aeff4f20b6706f98c9b3f641 |
| institution | Kabale University |
| issn | 1751-9675 1751-9683 |
| language | English |
| publishDate | 2022-04-01 |
| publisher | Wiley |
| record_format | Article |
| series | IET Signal Processing |
| spelling | doaj-art-38e5f028aeff4f20b6706f98c9b3f6412025-08-20T03:55:11ZengWileyIET Signal Processing1751-96751751-96832022-04-0116223223710.1049/sil2.12086Period and signal reconstruction from the curve of trains of samplesMarek W. Rupniewski0Institute of Electronic Systems Warsaw University of Technology Warsaw PolandAbstract A finite sequence of equidistant samples (a sample‐train) of a periodic signal can be identified with a point in a multidimensional space. Such a point depends on the signal, the sampling period, and the starting time of the sequence. If the starting time varies, then the corresponding point moves along a closed curve. We prove that this curve, that is, the set of all sample‐trains of a given length, determines the signal period, provided that the sampling period is known and is smaller than half of the signal period. The presented result is proved with the help of the theory of rotation numbers developed by Poincaré. We also prove that the curve of sample‐trains determines the signal up to a time shift, provided that the ratio of the sampling period to the period of the signal is irrational. A counterexample shows that the assumption on the incommensurability of the periods cannot be dropped. Eventually, we show how to estimate the period of a signal from a finite number of its sample‐trains.https://doi.org/10.1049/sil2.12086dynamical systemperiod estimationrotation numbersignal samplingtime delay embedding |
| spellingShingle | Marek W. Rupniewski Period and signal reconstruction from the curve of trains of samples IET Signal Processing dynamical system period estimation rotation number signal sampling time delay embedding |
| title | Period and signal reconstruction from the curve of trains of samples |
| title_full | Period and signal reconstruction from the curve of trains of samples |
| title_fullStr | Period and signal reconstruction from the curve of trains of samples |
| title_full_unstemmed | Period and signal reconstruction from the curve of trains of samples |
| title_short | Period and signal reconstruction from the curve of trains of samples |
| title_sort | period and signal reconstruction from the curve of trains of samples |
| topic | dynamical system period estimation rotation number signal sampling time delay embedding |
| url | https://doi.org/10.1049/sil2.12086 |
| work_keys_str_mv | AT marekwrupniewski periodandsignalreconstructionfromthecurveoftrainsofsamples |