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This paper considers differential phase-shift transmission over a bandlimited channel with specified phase and amplitude characteristics. The problem treated is the prediction of feasible data rates and corresponding error rates over such channels. An expression is given for the probability of error. This expression takes into account intersymbol and interchannel interference when differential phase-shift keying (DPSK) modulation is used. A distortion index which is a measure of phase error is defined, and the concept of phase opening is used which parallels the concept of eye opening commonly employed in the amplitude-shift keying (ASK) modulation. The analytical methods are applied to illustrate the effects of various parameters on the performance of a high data rate transmission system over a telephone line. Results indicate that for a carefully equalized line, a single-tone system should be used, and that higher order phase alphabets are to be preferred as the bit rate increases.