This letter proposes new estimations of fractional power spectral density (FrPSD) and fractional correlation function (FrCF) for nonuniform sampling of random signals with non-stationarity and limited bandwidths in the fractional Fourier domain. Unlike previous works, the developed FrPSD and FrCF estimations are capable of dealing with unknown sampling instants. In order to obtain them, we first formulate approximations of FrCF and FrPSD making use of uniform sampling instants. Then we convert the approximate FrPSD to a fractional filtered version of the FrPSD for the original random signal, which does not rely on the sampling instants. With such operations, we propose the FrPSD estimation to cancel the bias of FrPSD approximation by means of a fractional inverse filtering and thereby obtain a high accuracy of it. The FrCF estimation is proposed to be the inverse fractional Fourier transform of the FrPSD, and it serves as the fractional interpolation of the previously obtained approximation of the FrCF. Simulation results show the effectiveness of the proposed estimation methods.

中文翻译：

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非均匀采样的分数功率谱和分数相关估计

这封信提出了分数功率谱密度 (FrPSD) 和分数相关函数 (FrCF) 的新估计，用于对分数傅立叶域中具有非平稳性和有限带宽的随机信号进行非均匀采样。与以前的工作不同，开发的 FrPSD 和 FrCF 估计能够处理未知的采样时刻。为了获得它们，我们首先利用均匀采样时刻来制定 FrCF 和 FrPSD 的近似值。然后我们将近似的 FrPSD 转换为原始随机信号的 FrPSD 的分数滤波版本，它不依赖于采样时刻。通过这样的操作，我们提出了 FrPSD 估计，以通过分数逆滤波来消除 FrPSD 近似的偏差，从而获得较高的精度。FrCF 估计被提议为 FrPSD 的分数阶傅里叶逆变换，它用作先前获得的 FrCF 近似值的分数插值。仿真结果表明了所提出的估计方法的有效性。