向强, 黄勤珍. 线性正则变换域的窄带信号表示及其抽样理论[J]. 云南大学学报(自然科学版), 2015, 37(4): 491-499. doi: 10.7540/j.ynu.20140441
引用本文: 向强, 黄勤珍. 线性正则变换域的窄带信号表示及其抽样理论[J]. 云南大学学报(自然科学版), 2015, 37(4): 491-499. doi: 10.7540/j.ynu.20140441
XIANG Qiang, HUANG Qin-zhen. The representation of narrow-band signal in linear canonical transform domain and its sampling theorem[J]. Journal of Yunnan University: Natural Sciences Edition, 2015, 37(4): 491-499. DOI: 10.7540/j.ynu.20140441
Citation: XIANG Qiang, HUANG Qin-zhen. The representation of narrow-band signal in linear canonical transform domain and its sampling theorem[J]. Journal of Yunnan University: Natural Sciences Edition, 2015, 37(4): 491-499. DOI: 10.7540/j.ynu.20140441

线性正则变换域的窄带信号表示及其抽样理论

The representation of narrow-band signal in linear canonical transform domain and its sampling theorem

  • 摘要: 窄带信号广泛应用在雷达、声呐、通信、定位、生物医学工程等领域,传统的抽样理论已经研究了傅里叶变换域窄带信号的抽样和重构实现.线性正则变换(LCT)是傅里叶变换、分数阶傅里叶变换(FrFT)的推广形式,相应的抽样理论还不十分完善,因此有必要在LCT域重新研究窄带信号的抽样定理.从LCT的定义和性质入手,首先给出了信号基于LCT的Hilbert变换以及LCT域窄带信号的时域表示形式;然后在此基础上导出了LCT域窄带信号的抽样定理和重构实现公式,这些结论是传统窄带信号抽样理论在线性正则变换域的推广.最后,仿真实验进一步验证了结论的正确性.

     

    Abstract: Narrow-band signal are widely used in radar,sonar,communication,positioning,biomedical engineering and other fields.The sampling and reconstruction formula of narrow-band signal in the Fourier Transform domain have been studied in traditional sampling theorem.The Linear Canonical Transform (LCT) is a generalization of the Fourier Transform and the Fractional Fourier Transform (FrFT).And the sampling theories related to it have not been completed yet,so the sampling theorem for narrow-band signal needs to be restudied in the LCT domain.Starting from the definition and property of LCT,we first introduce the Hilbert transform related to LCT,then obtain the representation of narrow-band signal in LCT domain and based on it,we deduce sampling theorem and reconstruction formula for narrow-band signal with LCT.Our work is a generalization of the classical results and will enrich the theoretical system of the Linear Canonical Transform.Finally,simulation results further validate the correctness of the conclusion.

     

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