非广义平稳随机过程的Wiener-Khinchin定理
The Wiener-Khinchin Theorem for Non-wide Sense stationary Random Processes
摘要：
本文将Wiener-Khinchin定理推广到非广义平稳随机过程，即在一定的假设下，证明了任意随机过程的功率谱密度（PSD）等于时均自相关函数的傅里叶变换。我们使用的定理表明，bandlimitedness的PSD意味着bandlimitedness的广义PSD的某一类非WSS信号。这一事实使我们能够应用由Gardner导出的用于广义PSD的Nyquist准则。
英文摘要：
We extend the Wiener-Khinchin theorem to non-wide sense stationary (WSS) random processes, i.e. we prove that, under certain assumptions, the power spectral density (PSD) of any random process is equal to the Fourier transform of the time-averaged autocorrelation function. We use the theorem to show that bandlimitedness of the PSD implies bandlimitedness of the generalized-PSD for a certain class of non-WSS signals. This fact allows us to apply the Nyquist criterion derived by Gardner for the generalized-PSD.
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