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The transversal or time domain filter provides one approach to equalization of digital data transmission systems. Automating such an approach depends on finding a systematic method of setting the parameters (i.e., the multipliers) of the filter. In this paper a heuristic theory of the equalization obtainable by transversal filters is described. Based on this theory, a steepest-ascent hill-climbing algorithm is derived. Numerical results obtained using the algorithm are given for various transmission facilities, along with results obtained using a simplified nonoptimum but noniterative scheme. The theory also indicates that an additional improvement in performance is obtainable if a variable phase intercept is available. Thus a second element is introduced into the overall equalizer to produce a controllable but constant phase shift across the transmission band. Finally, the effect of inaccurate tap spacing is considered, and shown to produce generally small errors, and the problems in applying the results to multilevel vestigial sideband are discussed.