Dynamics of a bandpass sigma-delta modulator as a piecewise isometry

Author

Ashwin, P. ; Deane, J.H.B. ; Fu, X.-C.

Author_Institution

Sch. of Electron. Eng. IT & Math., Surrey Univ., Guildford, UK

Volume

3

fYear

2001

fDate

6-9 May 2001

Firstpage

811

Abstract

We examine a model for a bandpass ΣΔ modulator introduced by Feely and co-workers (1996). This is shown to have the dynamics of a piecewise isometry of a union of convex polygons on the plane by an appropriate transformation of the linearised parts into normal form. Using these we show that the periodically coded regions form a packing of the phase space by circles and we link this system to a number of similar ones. In particular we conjecture that for typical values of the parameter θ there is a positive measure set of points that have aperiodic codings

Keywords

band-pass filters; chaos; nonlinear network analysis; sigma-delta modulation; aperiodic codings; bandpass ΣΔ modulator; bandpass sigma-delta modulator; convex polygons; dynamics; linearised parts; periodically coded regions; phase space; piecewise isometry; Artificial intelligence; Band pass filters; Delta-sigma modulation; Electronic mail; Feedback loop; Frequency; Mathematical model; Mathematics; Particle measurements; Transfer functions;

fLanguage

English

Publisher

ieee

Conference_Titel

Circuits and Systems, 2001. ISCAS 2001. The 2001 IEEE International Symposium on

Conference_Location

Sydney, NSW

Print_ISBN

0-7803-6685-9

Type

conf

DOI

10.1109/ISCAS.2001.921456

Filename

921456