The Wiener-Khinchin Theorem for Non-wide Sense stationary Random Processes

Details The Wiener-Khinchin Theorem for Non-wide Sense stationary Random Processes The Wiener-Khinchin Theorem for Non-wide Sense stationary Random Processes

2009-04-03

arxiv.org/abs/0904.0602v1

Mathematics

Statistics Theory

4 pages, 2 figures

Scientific paper

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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