Difference between irregular chaotic patterns of second-order double-loop ΣΔ modulators and second-order interpolative bandpass ΣΔ modulators

Charlotte Yuk-Fan Ho, Bingo Wing-Kuen Ling and Joshua D. Reiss

Chaos, Solitons & Fractals, 2007, vol. 33, issue 5, 1777-1782

Abstract: In this paper, we find that, by computing the difference between two consecutive state vectors of second-order double-loop sigma-delta modulators (SDMs) and plotting one component of the subtracted vectors against the other component, irregular chaotic patterns will become two vertical lines. By multiplying a matrix on the subtracted vectors, it can be further transformed to two fixed points. However, second-order interpolative bandpass SDMs still exhibit chaotic behaviors after applying the same transformations. Moreover, it is found that the Lyapunov exponent of state vectors of second-order double-loop SDMs is higher than that of second-order interpolative bandpass SDMs, whereas the Lyapunov exponent of transformed vectors becomes negative infinity for second-order double-loop SDMs and increases for second-order interpolative bandpass SDMs. Hence, by examining the occurrence of chaotic behaviors of the transformed vectors of these two SDMs, these two SDMs can be distinguished from their state vectors and their transformed vectors without solving the state equations and knowing the information of input signals.

Date: 2007
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077906002384
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:33:y:2007:i:5:p:1777-1782

DOI: 10.1016/j.chaos.2006.03.042

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().