On Delta Modulation

Demand for the transmission of digital data grows apace as the computerization of our society continues. This demand, coupled with the many recent striking advances in solid state circuit technology and with new concepts of digital switching, assures an increased role for digital transmission systems in the near future. The existence of such systems in turn gives new importance to digital means of transmitting analog signals. This paper is concerned with one such means--delta modulation. 2101 2102 T H E BELL SYSTEM TECHNICAL JOURNAL, DECEMBER 1972 In its simplest form, as depicted in Fig. 1, the delta modulation transmitter approximates a continuous input signal X{t) by a staircase signal Z(t) that has treads of duration T and risers of height A. Every T seconds the staircase either rises one step or falls one step in order to approach X(t) at that instant more closely. At each rise or fall, the delta modulator emits a binary digit that specifies the direction of the step just taken. At the receiver, these transmitted binary digits are then used to reconstruct Z(t), or perhaps a smoothed version of it. This system was first described in the literature in 1952.1 Because of its extreme conceptual simplicity, and its relative ease of instrumentation, delta modulation has attracted the attention of theorists and experimentalists alike, and many studies of it and its generalizations have been undertaken in the ensuring years. Many of these have been concerned with calculation or measurement of the mean squared error suffered by signals transmitted by delta modulation and with determination of how this quantity varies with the parameters of the system.