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首页> 外文期刊>Signal processing >Analysis of A-stationary random signals in the linear canonical transform domain
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Analysis of A-stationary random signals in the linear canonical transform domain

机译：线性典范变换域中的A平稳随机信号分析

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Highlights•The generalized concept of A-stationarity for random signals associated with the LCT has been introduced.•The LCT correlation function and the LCT power spectral density for A-stationary random signals have been derived.•The A-Wigner-Ville distribution of the A-stationary random signals in the LCT domain has been presented.•The sampling theorem for A-stationary random signals in the LCT domain have been obtained.AbstractThe notion of stationarity associated with the Fourier transform plays an important roll in random signals theory. As the linear canonical transform (LCT) has been shown to be a powerful tool in signal processing, the theories and properties of random signals in the LCT domain have been extensively studied. However, there are no results published associated with the generalized concept of stationarity for random signals in the LCT domain. Hence in this paper, the detailed analysis ofA-stationary random signals in the LCT domain has been presented, which shows that for random signals are non-stationary in the standard formulation whereas can beA-stationary. First, the generalized concept ofA-stationarity for random signals associated with the LCT has been introduced. Based on the concept, the LCT correlation function and the LCT power spectral density forA-stationary random signals have been derived. Then, we have redefined the notion ofA-stationarity in terms of theA-Wigner–Ville distribution. In addition, the sampling theorem forA-stationary random signals have been obtained. Finally, the simulations and the potential applications are carried out to verify the validity and correctness of the proposed results.
机译： 突出显示 • 已引入了与LCT相关的随机信号的A平稳的广义概念。 • A-的LCT相关函数和LCT功率谱密度已经得出了平稳的随机信号。 • 已经提出了LCT域中A平稳随机信号的A-Wigner-Ville分布。 • A平稳样本定理已获得LCT域中的随机信号。 摘要 与傅立叶变换相关的平稳性概念在随机信号理论中起着重要的作用。由于线性规范变换（LCT）已被证明是信号处理中的强大工具，因此在LCT域中对随机信号的理论和性质进行了广泛的研究。但是，没有发布与LCT域中随机信号的平稳性广义概念相关的结果。因此，本文对LCT域中的 A -平稳随机信号进行了详细分析，结果表明，对于随机信号，标准公式中的信号是非平稳的，但可以 A -stationary。首先，引入了与LCT相关的随机信号 A -平稳的广义概念。基于该概念，推导了 A 平稳随机信号的LCT相关函数和LCT功率谱密度。然后，我们根据 A -Wigner-Ville分布重新定义了 A -平稳性的概念。另外，获得了 A -平稳随机信号的采样定理。最后，通过仿真和潜在的应用验证了所提出结果的有效性和正确性。

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