Abstract
A new formula for the coefficients of the prediction error filter for noncausal symmetric (centralized) linear prediction is presented. It is shown that when the signal is AR, the centralized filter reduces to a scaled product of the optimal forward and backward prediction error filters for the process. The result appears to be unique for linear prediction. For example, the symmetric noncausal Wiener filter for estimating a signal in noise has no such realization in terms of optimal causal filters.
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