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A technique is presented and illustrated for designing fixed or variable networks to filter nonstationary random signals. The technique may be used to select fixed or varying parameters of a specified linear filter or to determine a suitable filter configuration within the bounds of some constraint. Inasmuch as the ensemble mean-squared error (M.S.E.) is not an effective error criterion for this purpose, the integral of the weighted M.S.E., , is used. Necessary and sufficient conditions are determined for minimization of by filters with some rather general constraints, and three examples of the solution for these filters are given.