On the linear minimum-mean-squared-error estimation of an undersampled wide-sense stationary random process

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We consider the problem of linearly estimating, in the sense of minimum-mean-squared error, a wide-sense stationary process in noise given uniformly spaced samples where the sampling interval is such that significant aliasing occurs. We derive the corresponding aliased Wiener filter and provide a technique for determining a closed form for the necessary power spectral density functions. We conclude with an example where both signal and noise are modeled using a second-order innovations representation.