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arXiv · 1001.2955

Quiet sigma delta quantization, and global convergence for a class of asymmetric piecewise affine maps

Rachel Ward
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Abstract

In this paper, we introduce a family of second-order sigma delta quantization schemes for analog-to-digital conversion which are `quiet' : quantization output is guaranteed to fall to zero at the onset of vanishing input. In the process, we prove that the origin is a globally attractive fixed point for the related family of asymmetrically-damped piecewise affine maps. Our proof of convergence is twofold: first, we construct a trapping set using a Lyapunov-type argument; we then take advantage of the asymmetric structure of the maps under consideration to prove convergence to the origin from within this trapping set.

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Rachel Ward. 2010-07-15. Quiet sigma delta quantization, and global convergence for a class of asymmetric piecewise affine maps. https://doi.org/10.1088/0951-7715%2F23%2F9%2F007

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