This paper treats the convergence of adaptive LMS filters and, in particular, the adaptive line enhancer (ALE). The learning curves of such a filter are a sum of exponentially decaying modes with time constants given by the eigenvalues of the input correlation matrix and the relative initial magnitudes given by the projections of the filter on the eigenvectors. It is shown that, for large filter lengths, a simple correspondence may be set up between the discrete and continuous cases. Indexed by frequency, the eigenvalues of the correlation matrix correspond to the magnitude of the power spectrum, and the projections onto the eigenvectors to the filter transfer function. A detailed analysis is carried out for single pole spectra and evaluated through a computer simulation. In general, the techniques developed provide a physical context, i.e., the signal spectrum, in which to evaluate convergence. Thus, it is possible, with varying degrees of accuracy depending on knowledge of the input spectrum, to predict the convergence behavior of the system in general. (Author)