Sampling of bandlimited signals in the linear canonical transform domain
Sampling of bandlimited signals in the linear canonical transform domain
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DOI：
10.1007/s11760-011-0258-0
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发表时间：
2011-08
期刊：
影响因子：
--
通讯作者：
D. Wei;Q. Ran;Yuanmin Li
中科院分区：
文献类型：
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作者：
D. Wei;Q. Ran;Yuanmin Li
线性正则变换（LCT）已被证明是光学和信号处理的有力工具。研究了LCT域带限信号的采样问题。首先，我们提出了基于LCT的线性标准级数（LCS），它是傅立叶级数的一种推广模式。此外，LCS继承了LCT的所有优良特性。特别地，给出了LCS的Parseval关系，并利用它导出了LCT的采样定理。然后，利用复LCS的Parseval关系的推广形式，得到了带限信号在LCT域的采样展开式。这种重构方法的优点是可以直接推导出采样展开式，而不需要基于香农定理。
The linear canonical transform (LCT) has been shown to be a powerful tool for optics and signal processing. This paper investigates the sampling of bandlimited signals in LCT domain. First, we propose the linear canonical series (LCS) based on the LCT, which is a generalized pattern of Fourier series. Moreover, the LCS inherits all the nice properties from the LCT. Especially, the Parseval’s relation is presented for the LCS, which is used to derive the sampling theorem of LCT. Then, utilizing the generalized form of Parseval’s relation for the complex LCS, we obtain the sampling expansion for bandlimited signals in LCT domain. The advantage of this reconstruction method is that the sampling expansion can be deduced directly not based on the Shannon theorem.