In Analog-to-digital (A/D) conversion, signal decimation has been proven to greatly improve the efficiency of data storage while maintaining high accuracy. When one couples signal decimation with the \(\Sigma \Delta \) quantization scheme, the reconstruction error decays exponentially with respect to the bit-rate. We build on our previous result, which extended signal decimation to finite frames, albeit only up to the second order. In this study, we introduce a new scheme called adapted decimation, which yields polynomial reconstruction error decay rate of arbitrary order with respect to the oversampling ratio, and exponential with respect to the bit-rate.

中文翻译：

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任意数量的Sigma-Delta量化有限帧的自适应抽取

在模数（A / D）转换中，信号抽取已被证明可在保持高精度的同时大大提高数据存储效率。当一个信号抽取与\（\ Sigma \ Delta \）量化方案耦合时，重构误差相对于比特率呈指数衰减。我们以之前的结果为基础，该结果将信号抽取范围扩展到有限帧，即使仅达到二阶。在这项研究中，我们引入了一种称为自适应抽取的新方案，该方案相对于过采样率产生任意阶次的多项式重构误差衰减率，而相对于比特率则产生指数级的误差。