Isolation of a periodic component by singular wavelet decomposition
In this paper, we propose to use a discrete wavelet transform with a singular wavelet to isolate the periodic component from the signal. Traditionally, it is assumed that the validity condition must be met for a basic wavelet (the average value of the wavelet is zero). For singular wavelets, the val...
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| Format: | Article |
| Language: | English |
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Belarusian National Technical University
2020-09-01
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| Series: | Sistemnyj Analiz i Prikladnaâ Informatika |
| Subjects: | |
| Online Access: | https://sapi.bntu.by/jour/article/view/477 |
| _version_ | 1797873748837138432 |
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| author | V. M. Romanchak M. A. Hundzina |
| author_facet | V. M. Romanchak M. A. Hundzina |
| author_sort | V. M. Romanchak |
| collection | DOAJ |
| description | In this paper, we propose to use a discrete wavelet transform with a singular wavelet to isolate the periodic component from the signal. Traditionally, it is assumed that the validity condition must be met for a basic wavelet (the average value of the wavelet is zero). For singular wavelets, the validity condition is not met. As a singular wavelet, you can use the Delta-shaped functions, which are involved in the estimates of Parzen-Rosenblatt, Nadaraya-Watson. Using singular value of a wavelet is determined by the discrete wavelet transform. This transformation was studied earlier for the continuous case. Theoretical estimates of the convergence rate of the sum of wavelet transformations were obtained; various variants were proposed and a theoretical justification was given for the use of the singular wavelet method; sufficient conditions for uniform convergence of the sum of wavelet transformations were formulated. It is shown that the wavelet transform can be used to solve the problem of nonparametric approximation of the function. Singular wavelet decomposition is a new method and there are currently no examples of its application to solving applied problems. This paper analyzes the possibilities of the singular wavelet method. It is assumed that in some cases a slow and fast component can be distinguished from the signal, and this hypothesis is confirmed by the numerical solution of the real problem. A similar analysis is performed using a parametric regression equation, which allows you to select the periodic component of the signal. Comparison of the calculation results confirms that nonparametric approximation based on singular wavelets and the application of parametric regression can lead to similar results. |
| first_indexed | 2024-04-10T01:21:08Z |
| format | Article |
| id | doaj.art-d78944d6aa9b4c52875abd5bc5968503 |
| institution | Directory Open Access Journal |
| issn | 2309-4923 2414-0481 |
| language | English |
| last_indexed | 2024-04-10T01:21:08Z |
| publishDate | 2020-09-01 |
| publisher | Belarusian National Technical University |
| record_format | Article |
| series | Sistemnyj Analiz i Prikladnaâ Informatika |
| spelling | doaj.art-d78944d6aa9b4c52875abd5bc59685032023-03-13T09:47:41ZengBelarusian National Technical UniversitySistemnyj Analiz i Prikladnaâ Informatika2309-49232414-04812020-09-01034810.21122/2309-4923-2020-3-4-8360Isolation of a periodic component by singular wavelet decompositionV. M. Romanchak0M. A. Hundzina1Белорусский национальный технический университетБелорусский национальный технический университетIn this paper, we propose to use a discrete wavelet transform with a singular wavelet to isolate the periodic component from the signal. Traditionally, it is assumed that the validity condition must be met for a basic wavelet (the average value of the wavelet is zero). For singular wavelets, the validity condition is not met. As a singular wavelet, you can use the Delta-shaped functions, which are involved in the estimates of Parzen-Rosenblatt, Nadaraya-Watson. Using singular value of a wavelet is determined by the discrete wavelet transform. This transformation was studied earlier for the continuous case. Theoretical estimates of the convergence rate of the sum of wavelet transformations were obtained; various variants were proposed and a theoretical justification was given for the use of the singular wavelet method; sufficient conditions for uniform convergence of the sum of wavelet transformations were formulated. It is shown that the wavelet transform can be used to solve the problem of nonparametric approximation of the function. Singular wavelet decomposition is a new method and there are currently no examples of its application to solving applied problems. This paper analyzes the possibilities of the singular wavelet method. It is assumed that in some cases a slow and fast component can be distinguished from the signal, and this hypothesis is confirmed by the numerical solution of the real problem. A similar analysis is performed using a parametric regression equation, which allows you to select the periodic component of the signal. Comparison of the calculation results confirms that nonparametric approximation based on singular wavelets and the application of parametric regression can lead to similar results.https://sapi.bntu.by/jour/article/view/477вейвлетвейвлет-преобразованиеокно парзена-розенблаттанепараметрическая аппроксимацияядерная оценка надарая-ватсона |
| spellingShingle | V. M. Romanchak M. A. Hundzina Isolation of a periodic component by singular wavelet decomposition Sistemnyj Analiz i Prikladnaâ Informatika вейвлет вейвлет-преобразование окно парзена-розенблатта непараметрическая аппроксимация ядерная оценка надарая-ватсона |
| title | Isolation of a periodic component by singular wavelet decomposition |
| title_full | Isolation of a periodic component by singular wavelet decomposition |
| title_fullStr | Isolation of a periodic component by singular wavelet decomposition |
| title_full_unstemmed | Isolation of a periodic component by singular wavelet decomposition |
| title_short | Isolation of a periodic component by singular wavelet decomposition |
| title_sort | isolation of a periodic component by singular wavelet decomposition |
| topic | вейвлет вейвлет-преобразование окно парзена-розенблатта непараметрическая аппроксимация ядерная оценка надарая-ватсона |
| url | https://sapi.bntu.by/jour/article/view/477 |
| work_keys_str_mv | AT vmromanchak isolationofaperiodiccomponentbysingularwaveletdecomposition AT mahundzina isolationofaperiodiccomponentbysingularwaveletdecomposition |