In this thesis the performance and realization of adaptive digital filters with differentially coded signals have been studied. A general formula that realizes the LMS algorithm with differentially coded signals has been derived. We then used this formula for analysis and realization of LDM, ADM and ADPCM ADF``s. Efficient algorithms have been derived for the LDM ADF, ADM ADF and ADPCM ADF. In particular, we have proposed algorithms of LDM ADF and ADM ADF with a time-varying convergence factor of which the performance is superior to the cases of using a constant convergence factor. Then, applying these algorithms to channel equalization, we have studied the performances of the three systems both for the cases of using a time-varying and a constant convergence factor. It appears that the ADM ADF with a time-varying convergence factor is most desirable in consideration of both the system complexity and the sensitivity to the variation of input parameter values. However, if we consider the dynamic range and the sensitivity to the variation of parameter values as the important performance factors, the ADPCM ADF with a time-varying convergence factor is preferred to the other two systems. Also, we presented a method of hardware implementation of DM ADF and the algorithm of QAM equalizer using DM ADF.