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The prediction theory presented in this paper is an extension of the prediction theory of Zadeh and Ragazzini. It differs from their theory in that the nonrandom component of the input signal in the Zadeh-Ragazzini model is restricted to a polynomial of known degree . In the theory developed here, the nonrandom component of the input signal may be any arbitrary linear function of a subset of known analytic functions where the subset of functions are known a priori but the linear relationship need not be. As in the previous solution, the .determination of the impulsive admittance of the optimum predictor reduces to the solution of a modified Wiener-Hopf integral equation.