The design of optimum polynomial digital data smoothers (filters) is considered for linear and adaptive processing systems. It is shown that a significant improvement in performance can be obtained by using linear smoothers that take into account known a priori constraints or distributions of the input signal. The procedure for designing optimum (minimum mean square error) adaptive polynomial data smoothers is then discussed and analyzed. The optimum smoother makes use of a priori signal statistics combined with an adaptive Bayesian weighting of a bank of conditionally optimum smoothers. Use of this technique permits large improvements in performance with a minimum of additonal system complexity
