Nonlinear behaviors of bandpass sigma delta modulators with stable system matrices

Ling, Wing-Kuen and Ho, Yuk-Fan and Reiss, Joshua and Yu, Xinghuo (2005) Nonlinear behaviors of bandpass sigma delta modulators with stable system matrices. In: International Conference of Acoustics, Speech and Signal Processing, ICASSP, Philadelphia, USA.

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Official URL: http://dx.doi.org/10.1109/ICASSP.2005.1415948

Abstract

It has been established that a class of bandpass sigma delta modulators (SDMs) may exhibit state space dynamics which are represented by elliptical or fractal patterns confined within trapezoidal regions when the system matrices are marginally stable. In this paper, it is found that fractal patterns may also be exhibited in the phase plane when the system matrices are strictly stable. This occurs when the sets of initial conditions corresponding to convergent or limit cycle behavior do not cover the whole phase plane. Based on the derived analytical results, some interesting results are found. If the bandpass SDM exhibits periodic output, then the period of the symbolic sequence must equal the limiting period of the state space variables. Second, if the state vector converges to some fixed points on the phase portrait, these fixed points do not depend directly on the initial conditions.

Item Type:Conference or Workshop Item (Paper)
Additional Information:It has been established that a class of bandpass sigma delta modulators (SDMs) may exhibit state space dynamics which are represented by elliptical or fractal patterns confined within trapezoidal regions when the system matrices are marginally stable. In this paper, it is found that fractal patterns may also be exhibited in the phase plane when the system matrices are strictly stable. This occurs when the sets of initial conditions corresponding to convergent or limit cycle behavior do not cover the whole phase plane. Based on the derived analytical results, some interesting results are found. If the bandpass SDM exhibits periodic output, then the period of the symbolic sequence must equal the limiting period of the state space variables. Second, if the state vector converges to some fixed points on the phase portrait, these fixed points do not depend directly on the initial conditions.
Keywords:stable, nonlinear, chaos, limit cycle, bandpass, sigma delta modulator
Subjects:H Engineering > H310 Dynamics
Divisions:College of Science > School of Engineering
ID Code:3099
Deposited By:INVALID USER
Deposited On:05 Aug 2010 21:34
Last Modified:13 Mar 2013 08:43

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