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In recent work, a new version of an LMS algorithm has been developed which implements a variable feedback constant μ for each weight of an adaptive transversal filter. This technique has been called the VS (variable step) algorithm and is an extension of earlier ideas in stochastic approximation for varying the step size in the method of steepest descents. The method may be implemented in hardware with only modest increases in complexity ( percent) over the LMS Widrow-Hoff algorithm. It is shown that an upper bound for the convergence time is the classical mean-square-error time constant, and examples are given to demonstrate that for broad signal classes (both narrow-band and broad-band) the convergence time is reduced by a factor of up to 50 in noise canceller applications for the proper selection of variable step parameters. Finally, the VS algorithm is applied to an IIR filter and simulations are presented for applications of the VS FIR and IIR adaptive filters.