Smoothing as an improvement on filtering: a universal bound

Comparison is made between the mean-square errors Pf and Ps associated with the linear least-squares filtered and smoothed estimates of a stationary process of spectral density S(¿) in white noise of spectral density No. A universal curve is obtained which relates the minimum possible value of Ps/Pf to ¿max{S(¿) No}. The curve sets a bound on the maximum improvement over filtering which smoothing will offer, in terms of the maximum signal/noise ratio.