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Abstract This letter describes the performance characteristics of the LMS adaptive filter, a digital filter composed of a tapped delay line and adjustable weights, whose impulse response is controlled by an adaptive a-lgorithm. For stationary stochastic inputs, the mean-square error, the difference between the filter output and externally ~upplied input called the ”desired response”. is a quadratic function of the weights. In general, it can be shown that far stationary input and sufficiently small adaptive step size, the speed of convergence of the LMS algorithm i& dependent on the eigenvalue spread or the ratio of maximum eigenvalues to minimum eigenvalues (~max/~min), of the input data autocorrelation .. tr1.x. This ratio, often referred to as the ”condition number”, is a measure of ill-conditioning of the matrix. Slow convergence rate can be expected when this ratio is 14rqe. An approach to accelerate the convergence rate is to somehow transform the input signal RXn” into another Signal with corresponding autocorrelation matrix having smaller eigenvalue spread. This can be Achived by performing the adaptive filtering insome orthogonal transform domain. |