Wavelet transformation on a finite interval
Integral transformations on a finite interval with a singular basis wavelet are considered. Using a sequence of such transformations, the problem of nonparametric approximation of a function is solved. Traditionally, it is assumed that the validity condition must be met for a basic wavelet (the aver...
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| Format: | Article |
| Language: | Russian |
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National Academy of Sciences of Belarus, the United Institute of Informatics Problems
2021-01-01
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| Series: | Informatika |
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| Online Access: | https://inf.grid.by/jour/article/view/1060 |
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| _version_ | 1849240295681556480 |
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| author | V. M. Romanchak |
| author_facet | V. M. Romanchak |
| author_sort | V. M. Romanchak |
| collection | DOAJ |
| description | Integral transformations on a finite interval with a singular basis wavelet are considered. Using a sequence of such transformations, the problem of nonparametric approximation of a function is solved. Traditionally, it is assumed that the validity condition must be met for a basic wavelet (the average value of the wavelet must be zero). The paper develops the previously proposed method of singular wavelets when the tolerance condition is not met. In this case Delta-shaped functions that participate in Parzen – Rosenblatt and Nadaray – Watson estimations can be used as a basic wavelet. The set of wavelet transformations for a function defined on a numeric axis, defined locally, and on a finite interval were previously investigated. However, the study of the convergence of the decomposition on a finite interval was carried out only in one particular case. It was due to technical difficulties when trying to solve this problem directly. In the paper the idea of evaluating the periodic continuation of a function defined initially on a finite interval is implemented. It allowed to formulate sufficient convergence conditions for the expansion of the function in a series. An example of approximation of a function defined on a finite interval using the sum of discrete wavelet transformations is given. |
| format | Article |
| id | doaj-art-48b20e0c8f9240ccb02af53710909892 |
| institution | Kabale University |
| issn | 1816-0301 |
| language | Russian |
| publishDate | 2021-01-01 |
| publisher | National Academy of Sciences of Belarus, the United Institute of Informatics Problems |
| record_format | Article |
| series | Informatika |
| spelling | doaj-art-48b20e0c8f9240ccb02af537109098922025-08-20T04:00:40ZrusNational Academy of Sciences of Belarus, the United Institute of Informatics ProblemsInformatika1816-03012021-01-01174223510.37661/10.37661/1816-0301-2020-17-4-22-35942Wavelet transformation on a finite intervalV. M. Romanchak0Belarusian National Technical UniversityIntegral transformations on a finite interval with a singular basis wavelet are considered. Using a sequence of such transformations, the problem of nonparametric approximation of a function is solved. Traditionally, it is assumed that the validity condition must be met for a basic wavelet (the average value of the wavelet must be zero). The paper develops the previously proposed method of singular wavelets when the tolerance condition is not met. In this case Delta-shaped functions that participate in Parzen – Rosenblatt and Nadaray – Watson estimations can be used as a basic wavelet. The set of wavelet transformations for a function defined on a numeric axis, defined locally, and on a finite interval were previously investigated. However, the study of the convergence of the decomposition on a finite interval was carried out only in one particular case. It was due to technical difficulties when trying to solve this problem directly. In the paper the idea of evaluating the periodic continuation of a function defined initially on a finite interval is implemented. It allowed to formulate sufficient convergence conditions for the expansion of the function in a series. An example of approximation of a function defined on a finite interval using the sum of discrete wavelet transformations is given.https://inf.grid.by/jour/article/view/1060waveletwavelet transformthe parzen – rosenblatt window methodnonparametric estimatornadaraya − watson kernel regression |
| spellingShingle | V. M. Romanchak Wavelet transformation on a finite interval Informatika wavelet wavelet transform the parzen – rosenblatt window method nonparametric estimator nadaraya − watson kernel regression |
| title | Wavelet transformation on a finite interval |
| title_full | Wavelet transformation on a finite interval |
| title_fullStr | Wavelet transformation on a finite interval |
| title_full_unstemmed | Wavelet transformation on a finite interval |
| title_short | Wavelet transformation on a finite interval |
| title_sort | wavelet transformation on a finite interval |
| topic | wavelet wavelet transform the parzen – rosenblatt window method nonparametric estimator nadaraya − watson kernel regression |
| url | https://inf.grid.by/jour/article/view/1060 |
| work_keys_str_mv | AT vmromanchak wavelettransformationonafiniteinterval |