Stability Conditions for DPCM Coders

Differential pulse code modulation (DPCM) systems, used for encoding signals, are recursive and exhibit instability under certain conditions. In this paper, sufficient conditions for asymptotic stability of multidimensional DPCM systems are obtained both in the signal domain and the transform domain. In the case of instability, certain kinds of limit cycles, necessary conditions for their suppression are derived. The stability conditions are evaluated for one-, two-, and three-dimensional predictors.