Optimization based on a square-error criterion with an arbitrary weighting function

Several important criteria for the performance of communication systems and control systems are reviewed, and a new criterion (the mean-weighted-square-error criterion) is then introtroduced. This is shown to be a special form of a very general criterion proposed earlier, but to have special significance in that it is a generalization of the familiar mean-square-error criterion. The minimization of the mean-weighted-square error is treated in detail, and a solution for the optimum physically realizable frequency function of the system is given.