A detailed analysis of the performance the Wiener optimal filter for estimating a signal in additive noise is carried out. A first order AR model is assumed for both the signal and noise. Both IIR and FIR forms of the filter are considered and expressions are derived for the processing gain, mean square error and signal distortion. These measures are plotted as a function of the model parameters. This analysis motivates a generalized form of the Wiener filter, which can improve the signal distortion. An analysis of this more general filter is then carried out. A practical noise removal algorithm based on short time filtering using the generalized filter is also described, and results of applying the algorithm to some typical underwater acoustic data are presented.