Fractional Sampling Theorem for $\alpha$-Bandlimited Random Signals and Its Relation to the von Neumann Ergodic Theorem
Fractional Sampling Theorem for $\alpha$-Bandlimited Random Signals and Its Relation to the von Neumann Ergodic Theorem
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DOI：
10.1109/tsp.2014.2328977
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发表时间：
2014-07
影响因子：
5.4
通讯作者：
Rafael Torres;Z. Lizarazo;E. Torres
中科院分区：
文献类型：
--
作者：
Rafael Torres;Z. Lizarazo;E. Torres
考虑分数阶相关函数和分数阶功率谱密度，对于α平稳的随机信号，形成分数阶傅里叶变换对。基于α带宽受限随机信号的分数抽样定理，我们给出了一个从时间随机序列中估计随机信号的内插公式。此外，通过建立采样定理和von Neumann遍历定理之间的关系，从一个采样信号估计随机信号的功率谱密度成为一种合适的方法。因此，随机信号采样定理的有效性与均值意义上的遍历假设密切相关。
Considering that fractional correlation function and the fractional power spectral density, for α-stationary random signals, form a fractional Fourier transform pair. We present an interpolation formula to estimate a random signal from a temporal random series, based on the fractional sampling theorem for α-bandlimited random signals. Furthermore, by establishing the relationship between the sampling theorem and the von Neumann ergodic theorem, the estimation of the power spectral density of a random signal from one sample signal becomes a suitable approach. Thus, the validity of the sampling theorem for random signals is closely linked to an ergodic hypothesis in the mean sense.