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In this paper, we describe an efficient design procedure for designing FIR filters whose general structure consists of a transversal filter with tap coefficients restricted to -1, 0, or + 1 and cascaded with simple recursive sections. Due to the multiplication-free nature of this transversal filter, the configuration is particularly attractive from the standpoint of implementation with very simple hardware. Dynamic programming methods in conjunction with a mean-square error functional are presented to select the set of coefficient values for the taps. The approach is based on the assumption that the approximation sequence can be described as the output of a sequential machine whose state corresponds to the state-space representation of the sections in cascade with the transveral filter.