In this thesis, the performances of delta modulation systems have been studied when the input signal to the DM coder is a voice-band modulated data signal. First, the parameter values of three DM systems, linear delta modulation (LDM), constant factor DM(CFDM), and continuously variable slope DM(CVSD) have been optimized. Then the performances of the three DM systems have been studied in ideal and noisy channel When the multi-level DPSK signal is the input to each SM coder. It has been found that the peak SQNR is nearly the same regardless of coding scheme used, but CFDM yields the widest dynamic range. In noisy channel, however, CFDM is extensively sensitive to channel bit error. Thus, the use of CFDM appears to be not acceptable in the channel with an error rate above $10^{-4}$. Among the three DM systems, CVSD is found out to be the best regardless of the channel condition. In addition, the performance of DM has been compared with those of PCM and DPCM systems. The performance of SM is comparable with the $\mu$-law PCM and DPCM at the sampling rate of 48 Kbits/sec, and 32 Kbits/sec, respectively. Finally, two empirical formulas of LDM quantization noise have been obtained, which can be suitable to three DM systems by evaluating the effective step size of DM encoder.