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This paper analyses the behaviour of a second order DPCM (Differential PulseCode Modulation) transmission system when the nonlinear characteristic of thequantizer is taken into consideration. In this way, qualitatively newproperties of the DPCM system have been unravelled, which cannot be observedand explained if the nonlinearity of the quantizer is neglected. For thepurposes of this study, a piece-wise linear nondifferentiable quantizercharacteristic is considered. The resulting model of the DPCM is of the form ofiteration equations (i.e. map), where the inverse iterate is not unique (i.e.noninvertible map). Therefore the mathematical theory of noninvertible maps isparticularly suitable for this analysis, together with the more classic toolsof Non Linear Dynamics. This study allowed us in addition to show from atheoretical point of view some new properties of nondifferentiable maps, incomparison with differentiable ones. After a short review of noninvertiblemaps, the presented methods and tools for noninvertible maps are applied to theDPCM system. An original algorithm for calculation of bifurcation curves forthe DPCM map is proposed. Via the studies in the parameter and phase plane,different nonlinear phenomena such as the overlapping of bifurcation curvescausing multistability, chaotic behaviour, or multiple basins with fractalboundary are pointed out. All observed phenomena show a very complex dynamicalbehaviour even in the constant input signal case, discussed here.

Dynamical Study of a Second Order DPCM Transmission System Modeled by a Piece-Wise Linear Function