| Balance of multi-wavelets |
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| 作者姓名： | 毛一波 |
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| 作者单位： | MAO Yibo Department of Mathematics，Yuxi College，Yongchuan，Chongqing 402168，P.R. China Received 8 January 2003; revised 12 May 2003 |
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| 基金项目： | Supported by the Scientific Research Foundation for Returned Overseas Chinese Scholars from the State Education Ministry (No. [2002]247)，and the Young Key Teachers Foundation of Chongqing University. |
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| 摘 要： | 1. Introduction A multi-wavelet is a wavelet generated by a multi-scaling function consisting of several functions. Multi-wavelets have some advantages in practical application over scalar wavelets because they possess all these properties such as short support, orthogonality, symmetry and higher approximation order at the same time. But in practical application the discrete scalar data need prefiltering when they are transformed by discrete multi-wavelets. Prefiltering makes some pro-perties …
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Balance of multi-wavelets |
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| MAO Yibo.Balance of multi-wavelets[J].Journal of Chongqing University,2003,2(2). |
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| Authors: | MAO Yibo |
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| Institution: | Department of Mathematics, Yuxi College, Yongchuan, Chongqing 402168, P.R.China |
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| Abstract: | The discrete scalar data need prefiltering when transformed by discrete multi-wavelet, but prefiltering will make some properties of multi-wavelets lost. Balanced multi-wavelets can avoid prefiltering. The sufficient and necessary condition of p-order balance for multi-wavelets in time domain, the interrelation between balance order and approximation order and the sampling property of balanced multi-wavelets are investigated. The algorithms of 1-order and 2-order balancing for multi-wavelets are obtained. The two algorithms both preserve the orthogonal relation between multi-scaling function and multi-wavelets. More importantly, balancing operation doesnt increase the length of filters, which suggests that a relatively short balanced multi-wavelet can be constructed from an existing unbalanced multi-wavelet as short as possible. |
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| Keywords: | balanced multi-wavelets approximation order balancing algorithm sampling property |
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