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A filter estimates (predicts) the value of an unobserved random variable based on the values of a set of observed random variables. In the context of random processes, we desire a filter that, given an input X(t), produces an output Yˆ ðsÞ that best estimates Y(s), where goodness is based on an error measure between Yˆ ðsÞ and Y(s).
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