| 二元半规范双小波框架滤波器的构造 |
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| 引用本文： | 孟明会,崔丽鸿,白欣叶,王海峰.二元半规范双小波框架滤波器的构造[J].北京化工大学学报(自然科学版),2017,44(2):124-128. |
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| 作者姓名： | 孟明会 崔丽鸿 白欣叶 王海峰 |
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| 作者单位： | 北京化工大学理学院,北京,100029;北京化工大学理学院,北京,100029;北京化工大学理学院,北京,100029;北京化工大学理学院,北京,100029 |
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| 基金项目： | 大学生创新创业训练计划（zd2016058） |
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| 摘 要： | 多元双小波框架的构造由于其较大的自由度和计算的复杂性，一直是小波框架研究内容的难点问题之一。本文提出了一类具有规范滤波器的二元双小波框架的构造方案。具体地，对给定的一对低通滤波器组，利用混合酉扩展原理，首先建立可以生成半规范双小波框架的高通滤波器对的最小数目，然后根据滤波器和多相矩阵之间的关系，给出了构造双小波框架滤波器的具体方案。
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| 关 键 词： | 半规范双小波框架 混合酉扩展原理 模矩阵 多相矩阵 |
| 收稿时间： | 2016-10-23 |
Construction of semi-canonical wavelet bi-frame filters with two variables |
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| MENG MingHui,CUI LiHong,BAI XinYe,WANG HaiFeng.Construction of semi-canonical wavelet bi-frame filters with two variables[J].Journal of Beijing University of Chemical Technology,2017,44(2):124-128. |
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| Authors: | MENG MingHui CUI LiHong BAI XinYe WANG HaiFeng |
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| Institution: | Faculty of Science, Beijing University of Chemical Technology, Beijing 100029, China |
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| Abstract: | Due to the greater freedom and the complexity of calculation, the construction of multivariate wavelet bi-frames has always been one of the difficult problems in the study of wavelet frames. This paper gives a method for the construction of wavelet bi-frames having two variables with canonical filters. Specifically, for a pair of given lowpass filters, we first establish the smallest number of highpass filters which need be added to give a semi-canonical wavelet bi-frame filter by using the mixed unitary extension principle, and then we obtain the construction method based on the relationship between the filters and the polyphase matrix. |
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| Keywords: | semi-wavelet bi-frame mixed unitary extension principle modulation matrix polyphase matrix |
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