Three types of delta modulation digital filters (DMDF) have been studied. These are finite impulse response (FIR) linear delta modulation digital filter (LDMDF), FIR adaptive delta modulation digital filter (ADMDF), and infinite impulse response (IIR) LDMDF. The proposed FIR LDMDF requires smaller memory size and yields better output performance than the FIR LDMDF originally proposed by Peled and Liu 1. Also, the FIR ADMDF studied in this work yields better output performance than the other two FIR ADMDF``s investigated previously 4, 7. A method reducing computation time of FIR ADMDF have been introduced. The coefficients of FIR ADMDF have been optimized to reduce the effect of quantization noise due to A/D conversion on the output of the system. The use of this FIR ADMDF in speech transmission system have been investigated. In addition, we have studied realization of an IIR LDMDF and compared it with its equivalent FIR LDMDF in complexity and computation time. Finally, hardware designs of single-and multi-channel FIR ADMDF``s have been considered with emphasis on reduction of computation time.