Lattices sampling and sampling rate conversion of multidimensional bandlimited signals in the linear canonical transform domain
Lattices sampling and sampling rate conversion of multidimensional bandlimited signals in the linear canonical transform domain
复制标题
线性正则变换域多维带限信号的格子采样和采样率转换
DOI：
10.1016/j.jfranklin.2019.06.031
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发表时间：
2019-09
期刊：
影响因子：
--
通讯作者：
Li Yuan Min
中科院分区：
文献类型：
--
作者：
Wei Deyun;Yang Wenwen;Li Yuan Min
线性正则变换(LCT)已被证明是光学和信号处理的有力工具。关于这种变换的许多理论已为人所知，但关于LCT域中任意点阵采样的一致采样定理以及采样率转换理论仍有待确定。针对这些问题，本文对任意格型采样、可分矩阵采样和不可分矩阵采样进行了深入研究，得到了LCT域上的一致采样定理和采样率转换理论。首先，在LCT域推导了任意格子采样的离散时间信号的谱表达式。在此基础上，提出了两个矩阵之间的无混叠采样关系，并给出了有限带宽信号在LCT域的理想重构表达式。其次，为了进一步研究离散信号的采样率转换理论，定义了多维离散时间线性正则变换(MDTLCT)，以及MDTLCT的卷积。第三，推导了在LCT域通过整数矩阵进行多维内插和抽取的公式。然后，基于内插和抽取的结果，分析了有理矩阵在LCT域的采样率转换，包括频谱分析和时间域的公式。最后，给出了仿真结果和理论的潜在应用。
The linear canonical transform (LCT) has been shown to be a powerful tool for optics and signal processing. Many theories for this transform are already known, but the uniform sampling theorem, as well as the sampling rate conversion theory about arbitrary lattices sampling in the LCT domain are still to be determined. Focusing on these issues, this paper carefully investigates arbitrary lattices sampling, the sampling with separable matrices and nonseparable matrices, to obtain uniform sampling theorem and the sampling rate conversion theory in the LCT domain. Firstly, the spectral expression of the discrete-time signal sampled via arbitrary lattice is deduced in the LCT domain. Based on it we propose the alias-free sampling relationship between two matrices and present the perfect reconstruction expressions for bandlimited signals in the LCT domain. Secondly, for further research on discrete signals to obtain sampling rate conversion theory, we define the multidimensional discrete time linear canonical transform (MDTLCT), as well as the convolution for the MDTLCT. Thirdly, the formulas of multidimensional interpolation and decimation via integer matrices in the LCT domain are derived. Then, based on the results of interpolation and decimation, we make analyses of the sampling rate conversion via rational matrices in the LCT domain, including spectral analyses and the formulas in time domain. Finally, simulation results and the potential applications of the theories are also presented.
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影响因子：
3.9
作者：
A. Zayed
通讯作者：
A. Zayed
与线性正则变换相关的函数空间中信号的采样和重构
影响因子：
5.4
作者：
Shi, Jun;Liu, Xiaoping;Sha, Xuejun;Zhang, Naitong
通讯作者：
Zhang, Naitong
DOI：
10.1364/josaa.7.000092
发表时间：
1990-01-01
影响因子：
1.9
作者：
CHEUNG, KF;MARKS, RJ
通讯作者：
MARKS, RJ
DOI：
10.1007/978-3-540-74260-9_1
发表时间：
2007-08
期刊：
Fourth International Conference on Image and Graphics (ICIG 2007)
影响因子：
--
作者：
Alain Horé;D. Ziou;F. Deschênes
通讯作者：
Alain Horé;D. Ziou;F. Deschênes
DOI：
10.1007/s11760-011-0258-0
发表时间：
2011-08
期刊：
Signal, Image and Video Processing
影响因子：
--
作者：
D. Wei;Q. Ran;Yuanmin Li
通讯作者：
D. Wei;Q. Ran;Yuanmin Li