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Stability of the DPCM transmission system

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2 Author(s)
Macchi, O. ; Lab. des Signaux et Syst., CNRS-ESE, Gif-sur-Yvette, France ; Uhl, C.

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 popt 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

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Circuits and Systems II: Analog and Digital Signal Processing, IEEE Transactions on  (Volume:39 ,  Issue: 10 )