Stability of Adaptive Delta Modulation systems with memory

Abstract

It is well known that multiplicative Adaptive Delta Modulation (ADM) systems with a 1-bit memory are unstable if the adaptation parameters P and Q are such that PQ > 1 [Jayant, “Adaptive Delta Modulation with a 1-Bit Memory,” BSTJ 48 (Feb. 1969)]. Furthermore, for this class of ADM systems it has been generally accepted that the maximum signal-to-noise ratio (SNR) occurs at PQ = 1 and P = 1.5. Subsequently, Zetterberg et al. have shown (1) that such systems can be made to perform stably with PQ > 1, and (ii) that the point at which maximum SNR occurs is dependent upon the class of the input signal [Zetterberg and Uddenfelt, “Adaptive Delta Modulation with Delayed Decision,” IEEE Trans. Comm. COM-22 (Sept. 1974)]. Effectively, Zetterberg uses a limited step size to stabilize the ADM system with a 1-bit memory and PQ > 1. In this paper it is demonstrated that this form of ADM implementation can lead to the loss of low-energy signals, rendering the technique impractical for speech encoding. Alternative techniques are proposed for implementing ADM systems which are stable across a wide range of values for PQ and P. For speech, the maximum SNR is observed for values of P > 2.