Single-Integration, Adaptive Delta Modulation

In this paper, an equation is derived for the optimum signal-to-noise ratio (s/n) of a single-integration, adaptive delta modulator. Meansquare quantizing noise is a mathematically tractable quantity which appears to be a reasonably good measure of overall performance. It was felt that an understanding of the relationships between this quantity and the character of the input signal would be useful. The derivations and data presented here all contribute to this end. Other practical considerations, such as subjective evaluation, 1 transmission errors, 2 and tandem encoding, 3 have been discussed elsewhere. Several simulations 4 of single-integration, adaptive delta modulators on a variety of speech signals have produced s/n's near or below the performance estimate suggested in this paper. It is further suggested that this estimate is very close to the upper bound on the performance of such coders. The s/n formula also provides an explanation of the disparities between s/n's taken on sine waves and those obtained while coding speech signals. A block diagram of a single-integration, adaptive delta modulator is shown in Fig. 1. At the encoder, the difference between an input 1463