Stability analysis for several second-order Sigma—Delta methods of coarse quantization of bandlimited functions

摘要

We investigate the stability and robustness properties of a family of algorithms used to “coarsely quantize” bandlimited functions. The algorithms we will consider are one-bit second-orderΣΔA-quantization schemes and some modified versions of these. We prove that there exists a bounded region that remains positively invariant under the two-dimensional piecewise-affine discrete dynamical system associated with each of these quantizers. Moreover, this bounded region can be constructed so that it is robust under small changes in the quantizer. We also show some interesting properties of the resulting binary sequences.