Real-Valued Periodic Wavelets:Construction and Relation with Fourier Series

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Volume 17, Issue 5

Han-lin Chen, Xue Zhang Liang, Si Long Peng & Shao Liang Xiao

DOI:

J. Comp. Math., 17 (1999), pp. 509-522

Published online: 1999-10

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Abstract

In this paper, we construct the real-valued periodic orthogonal wavelets. The method presented here is new. The decomposition and reconstruction formulas involve only 4 terms respectively. It demonstrates that the formulas are simpler than that in other kinds of periodic wavelets. Our wavelets are useful in applications since it is real valued. The relation between the periodic wavelets and the Fourier series is also discussed.

Keywords

Periodic wavelet Multiresolution Fourier series Linear independence

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@Article{JCM-17-509, author = {}, title = {Real-Valued Periodic Wavelets:Construction and Relation with Fourier Series}, journal = {Journal of Computational Mathematics}, year = {1999}, volume = {17}, number = {5}, pages = {509--522}, abstract = { In this paper, we construct the real-valued periodic orthogonal wavelets. The method presented here is new. The decomposition and reconstruction formulas involve only 4 terms respectively. It demonstrates that the formulas are simpler than that in other kinds of periodic wavelets. Our wavelets are useful in applications since it is real valued. The relation between the periodic wavelets and the Fourier series is also discussed. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9121.html} }

TY - JOUR T1 - Real-Valued Periodic Wavelets:Construction and Relation with Fourier Series JO - Journal of Computational Mathematics VL - 5 SP - 509 EP - 522 PY - 1999 DA - 1999/10 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9121.html KW - Periodic wavelet KW - Multiresolution KW - Fourier series KW - Linear independence AB - In this paper, we construct the real-valued periodic orthogonal wavelets. The method presented here is new. The decomposition and reconstruction formulas involve only 4 terms respectively. It demonstrates that the formulas are simpler than that in other kinds of periodic wavelets. Our wavelets are useful in applications since it is real valued. The relation between the periodic wavelets and the Fourier series is also discussed.

Han-lin Chen, Xue Zhang Liang, Si Long Peng & Shao Liang Xiao. (1970). Real-Valued Periodic Wavelets:Construction and Relation with Fourier Series. Journal of Computational Mathematics. 17 (5). 509-522. doi:

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