Translations:Least-squares prediction and smoothing/17/en

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Let us now derive the least-squares prediction filter, and let denote this prediction filter. Such a filter uses the input signal’s past values to predict that signal’s future values. The input is the signal , and the desired output is the time-advanced version of the input. Let the prediction distance be given by the positive integer . The input to the filter is the input at present time n. The desired output is the input at the future time . The prediction filter is designed so that the output at the present time n is an optimum estimate of the future value . If this estimate is denoted by , the filter’s action can be represented by the convolution