有限标架上任意阶Sigma-Delta Quantization的自适应抽取
Adapted Decimation on Finite Frames for Arbitrary Orders of Sigma-Delta Quantization
摘要：
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的效率。当将信号抽取与$ΣΔ$量化方案相结合时，重构误差相对于比特率呈指数衰减。我们建立在我们以前的结果，扩展信号抽取到有限帧，虽然只有到二阶。在这项研究中，我们引入了一个新的方案，称为自适应抽取，它产生多项式重建误差衰减率的任意阶的过采样率，和指数的比特率。
英文摘要：
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 $ΣΔ$ quantization scheme, the reconstruction error decays exponentially with respect to the bit-rate. We build on our previous result, which extends 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 rate, and exponential with respect to the bit-rate.
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