Distortion in transmission channels causes intersymbol interference in digital communication systems. This distortion may be partially corrected at the receiver through the use of a tapped delay line having adjustable tap gain settings (transversal filter), The problem of minimizing distortion with a finite-length transversal filter is examined. In the region of small initial channel distortion where most existing systems operate, the best tap gain settings satisfy a set of simultaneous linear equations. For larger initial distortion, iterative techniques are required to find best gain settings. The distortion is shown to be a convex function of the tap gains, so mathematical programming techniques may be employed for optimization. The practical problem is that of evolving a logical strategy whereby the tap gains of the transversal filter may be set to optimum values. An easily implemented system for automatic equalization is described which makes use of a steepest-descent technique of minimization. The equalizer is automatically set prior to data transmission in a training period during which a series of test pulses is transmitted. Only polarity information is required, so digital logic may be used in the equalizer. For application to high-speed data transmission, great accuracies are required for the tap gain settings. Thus the problem of noise in the channel during equalization is quite important. The final error due to noise and channel distortion and the equalizer settling time are discussed and evaluated. Finally, the effect of a transversal filter equalizer in terms of the system frequency-domain characteristics is considered.