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

Ashwin, P., Deane, J. H. B. and Fu, X-C. (2001) Dynamics of a bandpass sigma-delta modulator as a piecewise isometry Proceedings of the 2001 IEEE International Symposium on Circuits and Systems, 2001, 3. pp. 811-814.

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Abstract

We examine a model for a bandpass sigma-delta 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 theta there is a positive measure set of points that have aperiodic codings

Item Type: Article
Additional Information: Ashwin, P., Deane, J.H.B., & Fu, X.-C. (2001). Dynamics of a bandpass sigma-delta modulator as a piecewise isometry. Proceedings of the 2001 IEEE International Symposium on Circuits and Systems, 2001, 3, 811-814. © 2001 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Mr Adam Field
Date Deposited: 27 May 2010 14:41
Last Modified: 23 Sep 2013 18:33
URI: http://epubs.surrey.ac.uk/id/eprint/1470

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