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Estimation of an initial condition of sigma-delta modulators via projection onto convex sets

By Charlotte Yuk-Fan Ho, Bingo Wing-Kuen Ling and Joshua D. Reiss


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

Topics: H651 Digital Circuit Engineering, G400 Computer Science
Publisher: IEEE Circuits and Systems society
Year: 2006
OAI identifier:

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