The linear MMSE estimation of an aliased random process

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 modelled as the output of a second-order linear system driven by white noise.