In this paper, we mainly investigate the nonuniform sampling for random signals which are bandlimited in the linear canonical transform (LCT) domain. We show that the nonuniform sampling for a random signal bandlimited in the LCT domain is equal to the uniform sampling in the sense of second order statistic characters after a pre-filter in the LCT domain. Moreover, we propose an approximate recovery approach for nonuniform sampling of random signals bandlimited in the LCT domain. Furthermore, we study the mean square error of the nonuniform sampling. Finally, we do some simulations to verify the correctness of our theoretical results.

中文翻译：

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线性正则变换域中带限随机信号的非均匀采样

在本文中，我们主要研究线性规范变换（LCT）域中带限的随机信号的非均匀采样。我们证明了在 LCT 域中对随机信号带限的非均匀采样等于在 LCT 域中的预滤波器后的二阶统计特征意义上的均匀采样。此外，我们为 LCT 域中带限的随机信号的非均匀采样提出了一种近似恢复方法。此外，我们研究了非均匀采样的均方误差。最后，我们做了一些模拟来验证我们的理论结果的正确性。