|
|||||
|
|
| 关于Parseval框架小波的刻画 | |
| 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. DOI: 10.3770/j.issn:1000-341X.2011.02.007 |
| 作者姓名： | 张新祥 吴国昌 |
| 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 |
| 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). |
| 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. |
| 关 键 词： | generalized low pass filter Pseudo-scaling function MRA Parseval frame wavelets |
| 收稿时间： | 2009-03-17 |
| 修稿时间： | 2009-06-30 |
The Characterization of Parseval Frame Wavelets |
|
| 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. DOI: 10.3770/j.issn:1000-341X.2011.02.007 | |
| Authors: | Xin Xiang ZHANG and Guo Chang WU |
| Affiliation: | College of Information, Henan University of Finance and Economics, Henan 450002, P. R. China |
| 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 $ntimes n$ 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. |
| Keywords: | generalized low pass filter Pseudo-scaling function MRA Parseval frame wavelets. |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ | |
| 点击此处可从《数学研究及应用》浏览原始摘要信息 | |
| 点击此处可从《数学研究及应用》下载全文 | |