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The problem of rapid automatic equalization of a highly distorting wireline channel is considered. An appropriate training signal received through the channel is processed by a 100-tap transversal filter comprising the equalizer and subsequently compared with a locally available properly synchronized reference signal. Errors between these two signals motivate a steepest descent (SD) controller to iteratively synthesize the equalizer's impulse response which tends to minimize the mean-squared error. Using matrix notation, a deterministic analysis leads to a mathematical block diagram of the equalizer system. A computer-simulated example demonstrates the effectiveness of the process in a specific case. The evolution of the equalizer's impulse response is summarized graphically in a "learning surface". Implementation considerations lead to a nearly optimal but considerably simplified system. Smoothing techniques allow for effective equalization in the presence of white additive noise. Experimental observations support predicted results.