A novel noncoherent receiver for M-ary differential phase-shift keying signals transmitted over intersymbol interference channels is presented. The noncoherent receiver consists of a linear equalizer and a decision-feedback differential detector. A significant performance gain over a previously proposed noncoherent receiver can be observed. For an infinite number of feedback symbols, the optimum equalizer coefficients can be calculated analytically, and the performance of the proposed receiver approaches that of a coherent linear minimum mean-squared-error equalizer. Moreover, a modified least mean square and a modified recursive least squares algorithm for adaptation of the equalizer coefficients are discussed.