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This paper discusses a new adaptive technique for system identification of a model with a sparse impulse response. The standard technique for adaptive identification uses a filter with adaptive coefficients that range from a coefficient for the zero delay tap through a coefficient for the largest delay tap that is assumed to be in the system. When the system to be modelled has a sparse impulse response, many of these coefficients will converge to zero, or very small values. Since each coefficient is updated in each iteration, a good deal of the adaptation is spent updating these unnecessary weights. The technique presented in this paper represents a new technique that serially adapts each delay tap value as well as the coefficient value. Thus, using this new technique the number of delay taps can be greatly reduced if the system has a sparse impulse response.