This part of the book deals with extraction of signal from noisy measured data. We have seen in Chap.  5 that the mean-square error is a useful criterion showing how good an estimation process is. Therefore, the mean-square error is taken as the fundamental criterion. The estimates that minimize the mean-square error are taken as the best, or optimum estimates, and are also referred to as the least mean-square (lms.) estimates. The case we considered firstly is a scalar (one-dimensional) parameter with a random distribution of its values. The optimum nonrecursive estimator derived in Sect. 6.1.1 is the scalar Wiener filter whose coefficients are solutions of the Wiener–Hopf equationWiener–Hopf equation. This is followed in Sect. 6.1.2 by the extension of scalar results to vector case. Additionally, in Sect. 6.1.3 the case of a stationary random time-varying signal is considered. It will be shown that the assumption of stationarity gives that the optimum Wiener filter is in fact time invariant linear dynamic system with the corresponding pulse-transfer function. A case of nonstationary multivariate random time-varying signal is discussed in Sect. 6.1.4. Finally, this is followed in Sect. 6.2 by the extension of discrete-timeWiener filterfor discrete-time stationary linear system results to the continuous-timeContinuousWiener filter stationaryWiener filterfor continuous-time stationary linear system signals.