On suppression of a sinusoidal signal in broad-band noise

In an estimator-subtractor configuration of the generalized adaptive line enhancer (ALE), a sinusoidal signal (in broad-band noise) is estimated by the two-sided and one-sided Wiener and linear prediction filters. For a fixed number of input samples, the estimation error in Wiener and prediction filters is shown to be minimum, when both future and past samples, not necessarily equal in numbers, are utilized in the present estimate of the signal. The error in the estimate of the signal by the two-sided Wiener filter is also shown to be equal to that by the optimized form of the well-known ALE.