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Publication . Article . 2020

Local transformations with a singular wavelet

V. M. Romanchak;
Open Access   Russian  
Published: 01 Mar 2020 Journal: Informatika, volume 17, issue 1, pages 39-46 (issn: 1816-0301, Copyright policy )
Publisher: The United Institute of Informatics Problems of the National Academy of Sciences of Belarus
The paper considers a local wavelet transform with a singular basis wavelet. The problem of nonparametric approximation of a function is solved by the use of the sequence of local wavelet transforms. Traditionally believed that the wavelet should have an average equal to zero. Earlier, the author considered singular wavelets when the average value is not equal to zero. As an example, the delta-shaped functions, participated in the estimates of Parzen – Rosenblatt and Nadara – Watson, were used as a wavelet. Previously, a sequence of wavelet transforms for the entire numerical axis and finite interval was constructed for singular wavelets. The paper proposes a sequence of local wavelet transforms, a local wavelet transform is defined, the theorems that formulate the properties of a local wavelet transform are proved. To confirm the effectiveness of the algorithm an example of approximating the function by use of the sum of discrete local wavelet transforms is given. 
Subjects by Vocabulary


Microsoft Academic Graph classification: Wavelet transform Zero (complex analysis) Mathematics Interval (mathematics) Basis (linear algebra) Nonparametric statistics Function (mathematics) Sequence Wavelet Applied mathematics


wavelet transform, singular wavelets, the parzen – rosenblatt window method, nonparametric estimator, nadaraya − watson kernel regression, Electronic computers. Computer science, QA75.5-76.95

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Article . 2020
Providers: DOAJ-Articles