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. In this study, similar results have been proven for finite unitarily generated frames. We have devised a process called alternative decimation on finite frames that is compatible with $\Sigma\Delta$ quantization up to the second order. In both cases, decimation results in exponential error decay with respect to the bit usage.

中文翻译：

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Sigma-Delta量化的有限帧抽取分析

在模数 (A/D) 转换中，信号抽取已被证明可以在保持高精度的同时大大提高数据存储效率。当将信号抽取与 $\Sigma\Delta$ 量化方案结合使用时，重构误差相对于比特率呈指数衰减。在这项研究中，对于有限的单一生成帧已经证明了类似的结果。我们设计了一种称为有限帧替代抽取的过程，该过程与高达二阶的 $\Sigma\Delta$ 量化兼容。在这两种情况下，抽取都会导致与比特使用相关的指数误差衰减。