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Unsolved Problems in Mathematical Systems and Control Theory by Vincent D. Blondel, Alexandre Megretski

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Problem 3.7

Delta-Sigma modulator synthesis

Anders Rantzer

Dept. of Automatic Control

Lund Institute of Technology

P.O. Box 118

SE-221 00 LUND, Sweden

rantzer@control.lth.se

1 DESCRIPTION OF THE PROBLEM

Delta-Sigma modulators are among the key components in modern electronics. Their main purpose is to provide cheap conversion from analog to digital signals. In the figure below, the analog signal r with values in the interval [-1, 1] is supposed to be approximated by the digital signal d that takes only two values, -1 and 1. One can not expect good approximation at all frequencies. Hence, the dynamic system D should be chosen to minimize the error f in a given frequency range

There is a rich literature on Delta-Sigma modulators. See [2, 1] and ...

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