Stability of the DPCM transmission system

Bounded input-bounded output stability of the differential pulse code modulation (DPCM) transmission system is investigated. The output is calculated by a nonlinear feedback loop. In the feedforward path the quantizer characteristic can be taken as continuous. It exhibits a threshold and has a linear part with a variable slope p greater than 1. In the feedback path the linear filter R is recursive. Stability of R is sufficient but not necessary to ensure stability of the DPCM system. Conditions for stability of an order 1 predictor are determined. Comparison with the classical concept of stability for linear systems displays three specific features of the DPCM case: 1) the conditions on the prediction coefficient are less stringent: 2) the kind of stability is weaker; and 3) the negative case has a better stability than the positive case. As a function of the quantizer slope, the maximum prediction coefficient exhibits a maximum. The corresponding value p_opt delimits two ranges. For smaller slopes the quantizer threshold effect degrades the stability. At the optimum, the range of stability is the same with and without the quantizer threshold