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An application of digital filtering to communication over a channel having amplitude and phase distortion in the frequency band occupied by the transmitted signal is presented. Described are a nonrecursive and a recursive digital filter which can serve as adaptive equalizers in compensating for the amplitude and phase distortion caused by the channel. The filter coefficients are adjusted automatically by the use of a test signal which is transmitted over the channel. The adjustment of the coefficients is carried out in the presence of noise with the aid of a steepest descent algorithm. The recursive filter, consisting of a comb filter in cascade with a bank of parallel two-pole filters, is shown to be especially suited for performing equalization. By choosing as a test signal sinusoids whose frequencies coincide with the poles of the two-pole filters, the coefficients of the recursive filter are easily adjusted.