When is DPCM a stable system?

The stability of the classical differential pulse code modulation (DPCM) transmission systems is considered in the sense of having a bounded prediction error e=s-sˆ for a bounded input s. The difficulty stems from the nonlinear and recursive nature of the predictor, due to the inclusion of quantization in the filtering loop that achieves prediction. The classical stability constraints of linear filters are currently imposed on the loop filter. It is shown that these constraints are unnecessarily restrictive. For instance, when the loop filter is a one-order cell, its unique coefficient can overcross the value 1. In the second-order case, the coefficients a₁, a₂ may lie outside the stability triangle. This is a consequence of the amplitude limitation at the quantizer output