A direct and exact method for computing the transfer function of the optimum smoothing filter

This note presents a general and exact rule for computing the transfer function of the optimum linear realizable smoothing (lag) filter from the Heaviside expansion of the optimum zero lag filter. The two standard approaches are: 1) transformation to the time domain and integration and 2) approximation of
e^{-\alphas}
.The proposed rule is more practical to implement than the first method and more accurate than the second.