New results are presented offering insight into the performance and optimization of linear and adaptive delta modulation, together with a comparison with pulse code modulation. The results are applied to three cases of practical importance: television, speech, and broadband signals.
The results presented can be grouped into the following three categories. First, a performance characterization of linear delta modulation (DM) is given. With the aid of certain empirical observations made from computer simulations, closed form expressions are found for granular noise, overload noise, and minimum quantization noise powers. These results permit the prediction of the optimum performance obtainable from DM at various bandwidth expansion factor values for many classes of signals. A defined quantity called the slope loading factor is usefully employed in the characterization of DM performance. It is shown that the slope loading factor is a normalizing variable when used to describe S/NQ performance. The optimum performance of DM with signals such as television and speech having an integrated spectrum exceeds that with a broadband signal having a uniform spectrum. It was also found that DM performance obtained with a Gaussian message signal amplitude probability density is essentially the same as that obtained with an exponential density.
Second, the advantages to be gained when adaptive control is introduced into the DM system are investigated. If the message signal ensemble is nonstationary, a companding function is required. It is shown that this may be provided in a DM system by forcing the step size to respond adaptively to changes in the derivative of the input signal. Adaptive DM may take either a discrete or continuous form. It is shown that discrete adaptive DM does not sacrifice optimum linear DM performance to achieve companding, and further that large values of companding improvement are possible. Because of the nonstationary nature of television and speech signals, it is concluded that adaptive DM appears better suited than linear DM to such signals. Finally, linear DM is shown to be a special case of discrete adaptive DM.
Third, the noise performance of PCM with Gaussian and exponential signal densities is presented together with a comparison between DM and PCM for television, speech, and broadband message signals. It is shown that the characteristic form of the performances of PCM and DM are similar when the independent variables are the amplitude loading factor and slope loading factor respectively. The effects of logarithmic companding and signal amplitude limiting on PCM performance are investigated. It has been found that adaptive DM appears capable of realizing a larger companding improvement than PCM, and that amplitude limiting in PCM is the counterpart of slope limiting in DM. For a television signal, it is concluded that DM provides a greater maximum S/NQ performance than PCM for values of the bandwidth expansion factor less than eight. For a speech signal, it is concluded that the performance of discrete adaptive DM with a bandwidth expansion factor value of four and a final gain factor value of only eight is approximately the same as that of companded PCM with a compression parameter value of one hundred. For a broadband signal, it is concluded that the performance of PCM is superior to that of DM. Finally, because of the complex nature of television and speech communication, it is concluded that subjective tests are needed before further conclusions regarding the performance advantages of discrete adaptive DM can be reached.
For an abridgment of the material in this dissertation, the reader is referred to a paper of the same title, written by the author, appearing in the Proceedings of the IEEE, March, 1967.
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