SYMBOLIC DYNAMICS OF PIECEWISE-LINEAR MAPS

In this paper we develop the theory of symbolic dynamics on piecewise- linear maps. We prove several results concerning periodic points and a dmissible periodic sequences and show how this theory is used on maps which are composed of signum functions by means of two examples in sig nal processing, namely digital filters with overflow nonlinearity and sigma-delta modulators. For example, we show that in the double-loop s igma-delta modulator with a two-bit quantizer, the set of initial cond itions which generate periodic output has zero measure for any constan t input, in contrast to the single-loop sigma-delta modulator.