| 关于Parseval框架小波的刻画 |
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| 引用本文： | 张新祥,吴国昌.关于Parseval框架小波的刻画[J].数学研究及应用,2011,31(2):242-250. |
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| 作者姓名： | 张新祥 吴国昌 |
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| 作者单位： | 河南财经政法大学信息学院, 河南 郑州 450002;河南财经政法大学信息学院, 河南 郑州 450002 |
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| 基金项目： | 国家自然科学基金(Grant No.60774041),河南省教育厅自然科学基金(Grant No.2010A110002). |
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| 摘 要： | In this paper,we characterize all generalized low pass filters and MRA Parseval frame wavelets in L 2 （R n ） with matrix dilations of the form （Df）（x） =√ 2f（Ax）,where A is an arbitrary expanding n × n matrix with integer coefficients,such that ｜det A｜ = 2.We study the pseudo-scaling functions,generalized low pass filters and MRA Parseval frame wavelets and give some important characterizations about them.Furthermore,we give a characterization of the semiorthogonal MRA Parseval frame wavelets and provide several examples to verify our results.
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| 关 键 词： | generalized low pass filter Pseudo-scaling function MRA Parseval frame wavelets |
| 收稿时间： | 2009/3/17 0:00:00 |
| 修稿时间： | 2009/6/30 0:00:00 |
The Characterization of Parseval Frame Wavelets |
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| Xin Xiang ZHANG and Guo Chang WU.The Characterization of Parseval Frame Wavelets[J].Journal of Mathematical Research with Applications,2011,31(2):242-250. |
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| Authors: | Xin Xiang ZHANG and Guo Chang WU |
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| Institution: | College of Information, Henan University of Finance and Economics, Henan 450002, P. R. China |
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| Abstract: | In this paper, we characterize all generalized low pass filters and MRA Parseval frame wavelets in $L^2(R^n)$ with matrix dilations of the form $(D f )(x) = \sqrt{2}f (Ax)$, where $A$ is an arbitrary expanding $n\times n$ matrix with integer coefficients, such that $|{\rm det}\,A| =2$. We study the pseudo-scaling functions, generalized low pass filters and MRA Parseval frame wavelets and give some important characterizations about them. Furthermore, we give a characterization of the semiorthogonal MRA Parseval frame wavelets and provide several examples to verify our results. |
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| Keywords: | generalized low pass filter Pseudo-scaling function MRA Parseval frame wavelets |
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