Fractional Fourier Analysis of Random Signals and the Notion of /spl alpha/-Stationarity of the Wigner - Ville Distribution
Fractional Fourier Analysis of Random Signals and the Notion of /spl alpha/-Stationarity of the Wigner - Ville Distribution
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DOI：
10.1109/tsp.2012.2236834
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发表时间：
2013-03
影响因子：
5.4
通讯作者：
Rafael Torres;E. Torres
中科院分区：
文献类型：
--
作者：
Rafael Torres;E. Torres
在本文中，提出了随机信号的广义α-平稳性的广义概念。平稳性的概念是随机信号傅立叶分析的基础。为此，引入了两个随机变量之间的分数相关性的定义。结果表明，对于广义α平稳随机信号，分数相关函数和分数功率谱密度函数形成分数傅里叶变换对。因此，α-平稳性的概念在通过分数阶傅立叶变换对标准公式中的信号非平稳但α-平稳的随机信号进行分析中起着重要作用。此外，我们根据分数相关函数定义了 α-Wigner-Ville 分布，其中标准傅里叶分析是 α = π/2 的特殊情况，并导出了 Wiener-Khinchin 定理。
In this paper, a generalized notion of wide-sense α-stationarity for random signals is presented. The notion of stationarity is fundamental in the Fourier analysis of random signals. For this purpose, a definition of the fractional correlation between two random variables is introduced. It is shown that for wide-sense α -stationary random signals, the fractional correlation and the fractional power spectral density functions form a fractional Fourier transform pair. Thus, the concept of α -stationarity plays an important role in the analysis of random signals through the fractional Fourier transform for signals nonstationary in the standard formulation, but α -stationary. Furthermore, we define the α-Wigner-Ville distribution in terms of the fractional correlation function, in which the standard Fourier analysis is the particular case for α = π/2 , and it leads to the Wiener-Khinchin theorem.