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An extension of the minimum mean square prediction theory for sampled input signals

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1 Author(s)

A method is developed for finding the ordinates of a digital filter which will produce a general linear operator of the signalS(t)such that the mean square error of prediction will be a minimum. The input to the filter is sampled at intervalsDelta t. The samples contain stationary noiseN(jDelta t), a stationary signal component,M(jDelta t), and a nonrandom signal component, begin{equation} P(jDelta t) = sum_{k=0}^n a_k P_k (jDelta t) end{equation} where the subset of nonrandom functionsP_k (t)are known a priori, but the parameter vectora = (a_o, a_l, cdots, a_n)need not be. The solution is obtained as a matrix equation which relates the ordinates of the digital filter to the autocorrelation properties ofM(t)andN(t)and the nature of the prediction operation.

Published in:

Information Theory, IRE Transactions on  (Volume:2 ,  Issue: 3 )

Date of Publication:

September 1956

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