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

@article{Ward2010QuietSD,
  title={Quiet sigma delta quantization, and global convergence for a class of asymmetric piecewise-affine maps},
  author={Rachel A. Ward},
  journal={Nonlinearity},
  year={2010},
  volume={23},
  pages={2165-2182}
}
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… 
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