Ho, Charlotte YukFan, Ling, Bingo WingKuen and Reiss, Joshua D. (2007) Difference between irregular chaotic patterns of secondorder doubleloop ΣΔ modulators and secondorder interpolative bandpass ΣΔ modulators. Chaos, Solitons and Fractals, 35 (3). pp. 17771782. ISSN 09600779
Full content URL: http://dx.doi.org/10.1016/j.chaos.2006.03.042
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Item Type:  Article 

Item Status:  Live Archive 
Abstract
In this paper, we find that, by computing the difference between two consecutive state vectors of secondorder doubleloop sigmadelta 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, secondorder interpolative bandpass SDMs still exhibit chaotic behaviors after applying the same transformations. Moreover, it is found that the Lyapunov exponent of state vectors of secondorder doubleloop SDMs is higher than that of secondorder interpolative bandpass SDMs, whereas the Lyapunov exponent of transformed vectors becomes negative infinity for secondorder doubleloop SDMs and increases for secondorder 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.
Additional Information:  In this paper, we find that, by computing the difference between two consecutive state vectors of secondorder doubleloop sigmadelta 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, secondorder interpolative bandpass SDMs still exhibit chaotic behaviors after applying the same transformations. Moreover, it is found that the Lyapunov exponent of state vectors of secondorder doubleloop SDMs is higher than that of secondorder interpolative bandpass SDMs, whereas the Lyapunov exponent of transformed vectors becomes negative infinity for secondorder doubleloop SDMs and increases for secondorder 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. 

Keywords:  SDM, Sinusoidal signals 
Subjects:  H Engineering > H620 Electrical Engineering H Engineering > H310 Dynamics 
Divisions:  College of Science > School of Engineering 
ID Code:  2676 
Deposited On:  13 Jun 2010 11:14 
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