The Application of Delta Modulation to Analog-to-PCM Encoding

Although delta modulation (AM) has been the subject of many theoretical and experimental studies, instances of its practical application are, to date, rare. In commercial systems, the most prominent digital representation of continuous signals is pulse code modulation (PCM). Relative to PCM, AM has the advantage of admitting simpler means of analog-to-digital and digital-to-analog conversion. However, the AM sampling rate is higher than that of PCM and in many cases the transmission rate is also higher. Since the discovery of delta modulation in the early 1950's, 1,2 in321 322 T H E BELL S Y S T E M TECHNICAL JOURNAL, FEBRUARY 1969 vestigators have proposed various modifications of the elementary, single-integration AM system (for example, double integration AM2, high information AM3, continuous AM 4 ) for the purpose of decreasing the required sampling rate. Generally, lower rates are achieved by means of operations on the continuous signals presented to and appearing in the delta modulator and thus at the expense of equipment complexity. In this paper we propose a P C M encoder that incorporates the simple single-integration delta modulator and a transversal digital filter that converts the AM sequence to a uniformly quantized PCM sequence. For this encoder, we demonstrate an inverse relationship between the AM sampling rate and the number of digital filter stages required to achieve a specified level of PCM quantizing noise power. With this encoder the advantages of AM, in particular the simple means of analog-to-digital conversion, may be combined with those of P C M : a linear representation of the continuous signal and in many cases a lower transmission rate than that required by simple AM.