Smoothing as an improvement on filtering in high noise (Q1080405)

This paper compares signal smoothing to signal filtering relative to estimation with a signal estimate to zero. Denoting \(P_ f\), \(P_ s\), \(P_ 0\) as the mean square errors associated with scalar filtering, smoothing, and a signal estimate of zero, we show that the performance improvement measure \(M\underline\triangle (P_ 0-P_ s)/(P_ 0-P_ f)\) increases monotonically from unity to two as the noise spectrum magnitude \(N_ 0\) increases from zero to infinity. This result is invariant of the signal spectrum assumed in \(L_ 1\). According to this measure M the maximum improvement of smoothing over filtering occurs in the high noise situation, underlying the desirability of smoothing in high noise.