Ho, Charlotte Yuk-Fan and Ling, Bingo Wing-Kuen and Reiss, Joshua D. (2006) Estimation of an initial condition of sigma-delta modulators via projection onto convex sets. IEEE Transactions on Circuits and Systems I: Regular Papers, 53 (12). pp. 2729-2738. ISSN 1057-7122

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Abstract

Abstract—In this paper, an initial condition of strictly causal rational interpolative sigma-delta modulators (SDMs) is estimated based on quantizer output bit streams and an input signal. A set of initial conditions generating bounded trajectories is characterized. It is found that a set of initial conditions generating bounded trajectories but not necessarily corresponding to quantizer output bit streams is convex. Also, it is found that a set of initial conditions corresponding to quantizer output bit streams but not necessarily generating bounded trajectories is convex too. Moreover, it is found that an initial condition both corresponding to quantizer output bit streams and generating bounded trajectories is uniquely defined if the loop filter is unstable (Here, an unstable loop filter refers to that with at least one of its poles being strictly outside the unit circle). To estimate that unique initial condition, a projection onto convex set approach is employed. Numerical computer simulations show that the employed method can estimate the initial condition effectively.

Item Type:	Article
Additional Information:	Abstract—In this paper, an initial condition of strictly causal rational interpolative sigma-delta modulators (SDMs) is estimated based on quantizer output bit streams and an input signal. A set of initial conditions generating bounded trajectories is characterized. It is found that a set of initial conditions generating bounded trajectories but not necessarily corresponding to quantizer output bit streams is convex. Also, it is found that a set of initial conditions corresponding to quantizer output bit streams but not necessarily generating bounded trajectories is convex too. Moreover, it is found that an initial condition both corresponding to quantizer output bit streams and generating bounded trajectories is uniquely defined if the loop filter is unstable (Here, an unstable loop filter refers to that with at least one of its poles being strictly outside the unit circle). To estimate that unique initial condition, a projection onto convex set approach is employed. Numerical computer simulations show that the employed method can estimate the initial condition effectively.
Keywords:	Sigma-delta modulators, Stability, Admissibility
Subjects:	H Engineering > H651 Digital Circuit Engineering G Mathematical and Computer Sciences > G400 Computer Science
Divisions:	College of Sciences > Faculty of Science > Lincoln School of Engineering
Depositing User:	Bev Jones
Date Deposited:	13 Jun 2010 12:03
Last Modified:	13 Mar 2013 08:39
URI:	http://eprints.lincoln.ac.uk/id/eprint/2687

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