Fractional Spectrum Analysis for Nonuniform Sampling in the Presence of Clock Jitter and Timing Offset
Fractional Spectrum Analysis for Nonuniform Sampling in the Presence of Clock Jitter and Timing Offset
复制标题
存在时钟抖动和定时偏移时的非均匀采样的分数频谱分析
DOI：
10.1109/tsp.2020.3007360
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发表时间：
2020
影响因子：
5.4
通讯作者：
Xuejing Kang
中科院分区：
文献类型：
--
作者：
Jinming Ma;Ran Tao;Yongzhe Li;Xuejing Kang
重点分析了时钟抖动和定时偏差对非均匀采样分数阶谱的影响。研究了分数阶傅里叶域中带宽有限的单通道采样和递归采样两种情况下的离散分数阶傅立叶变换。对于第一类DTFrFT，我们进行了统计分析，同时建立了非理想单/多通道模数转换器输入和输出信号的分数谱之间的关系。这种关系表明，每个分数频谱的统计平均值包含输入信号的频谱的周期性副本，并且这些副本特别地被时钟抖动引入的扰动的特征函数调制。此外，我们还从线性调频信号分解的角度对非均匀采样的第一类DTFrFT进行了解释。第二类DTFrFT是一种近似DTFrFT，特别适用于非均匀采样时刻未知的一般情况。为此，我们研究了具有已知核输入的第一类DTFrFT的修正形式，并在此基础上导出了两种情况下的近似分数谱的统计平均值。然后，我们通过开发最优的滤波器来高精度地补偿分数谱偏差，以最小化两种情况下原始频谱和补偿后的分数谱之间的均方误差。与单通道采样不同的是，递归采样的补偿在最优滤波之前增加了一个步骤，从而提供了更好的精度。仿真结果表明，该方法的性能优于已有方法。
This paper focuses on analyzing the fractional spectrum of nonuniform sampling which is affected by clock jitter and timing offset. Both cases of single-channel and recurrent samplings with limited bandwidth in the fractional Fourier domain are considered, for which we study two types of discrete-time fractional Fourier transforms (DTFrFTs). For the first-type DTFrFTs, we perform their statistical analyses, and meanwhile establish relationships between the fractional spectra of the input and output signals of non-ideal single/multi-channel analog-to-digital converter. Such relationships indicate that the statistical mean of each fractional spectrum contains periodic replicas of the spectrum for the input signal, and these replicas are particularly modulated by the characteristic function of the perturbations introduced by the clock jitter. Moreover, we interpret the first-type DTFrFTs from the perspective of linear frequency modulation signal decomposition for nonuniform sampling. The second-type DTFrFTs serve as approximate DTFrFTs, and they especially deal with the general situation when the nonuniform sampling instants are unknown. To this end, we study modified forms of the first-type DTFrFTs with known inputs in kernels, based on which the statistical mean of the approximate fractional spectra for both cases are derived. Then we compensate the fractional spectrum bias with high accuracy by developing optimal filters that minimize the mean square error between the original and the compensated fractional spectra for both cases. Different from single-channel sampling, the compensation for recurrent sampling involves an additional step before optimal filtering, which gives better accuracy. Simulation results show that the proposed methods outperform existing methods.