Several of the main digital communication systems in use today are surveyed. Particular attention is paid to the transmission of the speech signal. The autocorrelation and covariance formulations of linear predictive coding are compared for varying length segments of synthetically produced vowel sounds. The two formulations are also compared on vowel sounds contaminated with varying amounts of additive white noise. The two formulations were found to be roughly equivalent in their abilities to extract Z-plane pole locations from a signal. The autocorrelation method was shown to be computationally faster, however. A new pole extraction algorithm is tested in which the covariance method is used on several short over-lapping segments and a "cluster" decision scheme is used. This computationally expensive algorithm proves to yield better results than a straight forward application of the covariance method.