Ling, WingKuen and Ho, YukFan and Reiss, Joshua (2006) Estimation of initial states of sigmadelta modulators. In: 120th Convention of Audio Engineering Society, May 2006, Paris.
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Item Type:  Conference or Workshop contribution (Paper) 

Item Status:  Live Archive 
Abstract
In this paper, an initial condition of a sigmadelta modulator is estimated based on quantizer output bit streams and an input signal. The set of initial conditions that generate a stable trajectory is characterized. It is found that this set, as well as the set of initial conditions corresponding to the quantizer output bit streams, are convex. Also, it is found that the mapping from the set of initial conditions to the stable admissible set of quantizer output bit streams is invertible if the loop filter is unstable. Hence, the initial condition corresponding to given stable admissible quantizer output streams and an input signal is uniquely defined when the loop filter is unstable, and a projection onto convex set approach is employed for approximating the initial condition.
Additional Information:  In this paper, an initial condition of a sigmadelta modulator is estimated based on quantizer output bit streams and an input signal. The set of initial conditions that generate a stable trajectory is characterized. It is found that this set, as well as the set of initial conditions corresponding to the quantizer output bit streams, are convex. Also, it is found that the mapping from the set of initial conditions to the stable admissible set of quantizer output bit streams is invertible if the loop filter is unstable. Hence, the initial condition corresponding to given stable admissible quantizer output streams and an input signal is uniquely defined when the loop filter is unstable, and a projection onto convex set approach is employed for approximating the initial condition. 

Keywords:  estimation, initial state, sigma delta modulator, chaos, limit cycle 
Subjects:  H Engineering > H310 Dynamics 
Divisions:  College of Science > School of Engineering 
ID Code:  3100 
Deposited On:  05 Aug 2010 21:24 
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