The paper treats linear and nonlinear methods that refine the delta modulation process. These methods improve the quality of the decoded signal at a given transmission rate. Two linear processes are analyzed. The first one matches the source signal to the coder for minimum weighted noise in the decoded signal. The second one influences the signal which is fed to the comparator; it shapes the spectrum of the quantization noise desirably. Two nonlinear methods used in the delta modulation process are discussed. The first achieves a best possible prediction of the future signal from past binary decisions and thus a reduction of the error signal. The methods of the second type make the coder adaptive to variations in the power level of the source signal. This results in a large dynamic range of the coding system. A comparison of the various methods is made and a coding system for speech signals, based on a suitable combination of these methods, is described. Copyright © 1974 by The Institute of Electrical and Electronics Engineers, Inc.