Abstract
When the Nyquist property is not fulfilled, uniform sampling does not give enough information to perform errorless reconstruction. Furthermore, errors depend on the device which takes the samples. For example, the samples can be obtained averaging the process around periodic times. More generally, samples can be deduced from linear filtering of functions or random processes. This paper addresses the problem of finding the optimal linear filter which minimizes the mean time error in the context of stationary processes. It will be shown that this problem has simple solutions, whatever the power spectrum width of the studied process.
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