## Electrical and Computer Engineering ETDs

## Publication Date

6-1968

## Abstract

This thesis is a study of certain aspects of delta modulation which are of particular interest or significance in control system communication. Delta Modulation is a discrete difference encoding method in which the amplitude difference between the signals occurring at two points in time can be transmitted as a plus one or a minus one bit. Such a method of encoding has a rate of change capacity limit rather than a hard amplitude bound.

A determination of the sampling rates, and therefore bit rates, necessary to encode several types of signals is reported. Signals which themselves have a rate-limited characteristic are easily matched by the delta modulator rate capacity limit. Random signals, specifically first and second order Butterworth random processes, are analyzed in terms of their expected rates of change or their mean square sampleto-sample amplitude differences. The delta modulator can then be designed such that these signals can be encoded to a prescribed accuracy or level of distortion. It is shown that the required sampling rate is generally far greater than the "Nyquist" rate usually assumed.

Delta modulators can be constructed which employ either an ideal integration of past samples (perfect-memory) or approximate integration (imperfect-memory) in order to generate the encoded difference. The first case generally is impractical because any errors incurred during the transmission process have a permanent effect in the decoder or demodulator. The use of an imperfect-memory makes it possible to transmit signals in a useful manner in the presence of transmission medium noise. This noise is assumed to invert 1 s and O s at varying error rates or in bursts. The effect upon the demodulator output is described quantitatively as a function of various integrator memory times. It is shown that performance in noise can be improved by increasing the bit rate. In addition to the effects of external noise, the encoding process generates a certain amount of inherent noise. This is often referred to as quantizing noise in discrete level encoding systems. Expressions for this noise are presented, some of which are substantiated by experimental results. A model is presented which describes the delta modulator/ demodulator pair input-output characteristic as a noise generator and a transport delay. This model provides the designer with useful information for determining the applicability of delta modulation to a given situation.

## Document Type

Thesis

## Language

English

## Degree Name

Electrical Engineering

## Department Name

Electrical and Computer Engineering

## First Committee Member (Chair)

Daniel P. Petersen

## Second Committee Member

Harold Knud Knudsen

## Third Committee Member

Illegible

## Fourth Committee Member

Ahmed Erteza

## Recommended Citation

Maschhoff, Robert H.. "A Study Of Delta Modulation And Its Application To Control Communication." (1968). https://digitalrepository.unm.edu/ece_etds/619