A time domain synthesis for optimum extrapolators

A direct method is presented for the solution of the integral equation for the optimum predictor in terms of the solution to the integral equation for the optimum filter. This method is a means for circumventing the practical difficulties encountered in the actual design of optimum predictors based upon the techniques derived by Wiener. The synthesis procedure is applied in order to simplify the design of extrapolators for use when the prediction interval is a non-negative function of time in contrast to the more conventional situation where prediction is made for a continuously varying instant that is always a fixed number of seconds in the future. The specific example utilized is prediction for a fixed instant that is a continuously decreasing number of seconds in the future. The discussion includes an explanation of a procedure for avoiding the solution of integral equations in the synthesis of optimum extrapolators.