Linear predictor with a new error criterion

In the conventional linear predictor the nth sample is predicted as a linear combination of the previous p samples. In this paper we seek the prediction of the nth sample as a linear combination of certain filtered signals. The normal equations for this modified form of predictor are derived and a window function, suitable for this new formulation, is proposed. For brevity we will consider only deterministic signals. The advantages of this modified linear predictor are demonstrated by an example.