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It is well known that the time constants governing the learning curves of LMS adaptive filters are determined by the eigenvalues of the input correlation matrix. In this paper it is shown that for sufficiently long filters, a transformation to the frequency domain diagonalizes the matrix. As a consequence it is possible to obtain a simple representation of the spectrum of the LMS filter as a function of time (i.e., during convergence). The theoretical results are compared with a computer simulation.