Estimation of initial states of sigma-delta modulators

Ling, Wing-Kuen and Ho, Yuk-Fan and Reiss, Joshua (2006) Estimation of initial states of sigma-delta modulators. In: 120th Convention of Audio Engineering Society, May 2006, Paris.

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Abstract

In this paper, an initial condition of a sigma-delta 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.

Item Type:Conference or Workshop Item (Paper)
Additional Information:In this paper, an initial condition of a sigma-delta 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 By:INVALID USER
Deposited On:05 Aug 2010 21:24
Last Modified:13 Mar 2013 08:43

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