子空间混合有理时频多窗口伽柏框架及其伽柏对偶框架。
Subspace mixed rational time-frequency multiwindow Gabor frames and their Gabor duals.
作者信息
Zhang Yan, Li Yun-Zhang
机构信息
1School of Mathematics and Information Science, North Minzu University, Yinchuan, P.R. China.
2College of Applied Sciences, Beijing University of Technology, Beijing, P.R. China.
出版信息
J Inequal Appl. 2018;2018(1):280. doi: 10.1186/s13660-018-1876-7. Epub 2018 Oct 11.
For a usual multiwindow Gabor system, all windows share common time-frequency shifts. A mixed multiwindow Gabor system is one of its generalizations, for which time-frequency shifts vary with the windows. This paper addresses subspace mixed multiwindow Gabor systems with rational time-frequency product lattices. It is a continuation of (Li and Zhang in Abstr. Appl. Anal. 2013:357242, 2013; Zhang and Li in J. Korean Math. Soc. 51:897-918, 2014). In (Li and Zhang in Abstr. Appl. Anal. 2013:357242, 2013) we dealt with discrete subspace mixed Gabor systems and in (Zhang and Li in J. Korean Math. Soc. 51:897-918, 2014) with ones. In this paper, using a suitable Zak transform matrix method, we characterize subspace mixed multiwindow Gabor frames and their Gabor duals, obtain explicit expressions of Gabor duals, and characterize the uniqueness of Gabor duals. We also provide some examples, which show that there exist significant differences between mixed multiwindow Gabor frames and usual multiwindow Gabor frames.
对于一个普通的多窗口伽柏系统，所有窗口共享共同的时频偏移。混合多窗口伽柏系统是其一种推广形式，其中时频偏移随窗口而变化。本文研究具有有理时频乘积格的子空间混合多窗口伽柏系统。它是（Li和Zhang，《抽象与应用分析》，2013年：357242，2013；Zhang和Li，《韩国数学会杂志》，51：897 - 918，2014）的延续。在（Li和Zhang，《抽象与应用分析》，2013年：357242，2013）中我们处理了离散子空间混合伽柏系统，在（Zhang和Li，《韩国数学会杂志》，51：897 - 918，2014）中处理了[此处原文缺失信息]。在本文中，我们使用合适的扎克变换矩阵方法，刻画了子空间混合多窗口伽柏框架及其伽柏对偶，得到了伽柏对偶的显式表达式，并刻画了伽柏对偶的唯一性。我们还给出了一些例子，表明混合多窗口伽柏框架与普通多窗口伽柏框架之间存在显著差异。
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