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Volume 17, Issue 5
Real-Valued Periodic Wavelets: Construction and Relation with Fourier Series

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

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 those 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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COPYRIGHT: © Global Science Press

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@Article{JCM-17-509, author = {Chen , Han-LinLiang , Xue-ZhangPeng , Si-Long and Xiao , Shao-Liang}, 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 those 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 AU - Chen , Han-Lin AU - Liang , Xue-Zhang AU - Peng , Si-Long AU - Xiao , Shao-Liang 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, Multiresolution, Fourier series, 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 those 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.

Chen , Han-LinLiang , Xue-ZhangPeng , Si-Long and Xiao , Shao-Liang. (1999). Real-Valued Periodic Wavelets: Construction and Relation with Fourier Series. Journal of Computational Mathematics. 17 (5). 509-522. doi:
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