Symbolic dynamics of piecewise-linear maps

Author

Wu, Chai Wah ; Chua, Leon O.

Author_Institution

Dept. of Electr. Eng. & Comput. Sci., California Univ., Berkeley, CA, USA

Volume

41

Issue

6

fYear

1994

fDate

6/1/1994 12:00:00 AM

Firstpage

420

Lastpage

424

Abstract

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

Keywords

analogue-digital conversion; delta modulation; digital filters; filtering and prediction theory; piecewise-linear techniques; symbol manipulation; admissible periodic sequences; digital filters; double-loop sigma-delta modulator; nonlinear signal processing; overflow nonlinearity; periodic points; piecewise-linear maps; signum functions; single-loop sigma-delta modulator; symbolic dynamics; two-bit quantizer; zero measure; Circuits; Delta-sigma modulation; Digital filters; Digital modulation; Digital signal processing; Nonlinear dynamical systems; Particle measurements; Piecewise linear techniques; Signal analysis;

fLanguage

English

Journal_Title

Circuits and Systems II: Analog and Digital Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1057-7130

Type

jour

DOI

10.1109/82.300203

Filename

300203