A method is surveyed for telephone communication using a predictive adaptive delta modulator. This method is based on an estimation of the input waveform and an encoding of the signal into a digital sequence. The Kalman Filter does this estimation to filter out some of the noise, thus increasing the fidelity of the output to the original signal. The adaptive delta modulator does the encoding and allows the digital output to be reconstructed by a decoder which is identical to the feedback portion of the encoder. In implementing the adaptive delta modulator, a bi-state quantizer and tri-state quantizer are presented for comparison. Since the grannular region difficulties can be eliminated by the tri-state quantizer, the tri-state quantizer ADM provides a better stability. The present design also consists of a predictor which is based on the theory of a Taylor series expansion in order to match the overload rate whenever the signal slope becomes too sharp. The results indicate that the present design is suitable for implementation when the incoming messages are highly correlated-implying rapid signal sampling. / Master of Science