论文标题
二阶连续时间sigma-delta调制器中的错误估计值
Error estimates in Second-order Continuous-Time Sigma-Delta modulators
论文作者
论文摘要
连续时间sigma-delta（CT- $σδ$）调节器是对模数转换器的过度采样，这些转换器可能会提供更高的采样率和更低的功耗。尽管在高阶离散时间$σδ$调节器中建立了近似误差，但对过滤输出和输入之间误差的理论分析仍然很少。本文提出了一个研究此错误的一般框架：在输入和过滤内核的规律性假设下，我们证明了二阶Ct- $σδ$，该错误估计可能在$ O（1/N^2）$中，其中$ n $是$ n $的偏移率。整个理论通过数值实验验证。
Continuous-time Sigma-Delta (CT-$ΣΔ$) modulators are oversampling Analog-to-Digital converters that may provide higher sampling rates and lower power consumption than their discrete counterpart. Whereas approximation errors are established for high-order discrete time $ΣΔ$ modulators, theoretical analysis of the error between the filtered output and the input remain scarce. This paper presents a general framework to study this error: under regularity assumptions on the input and the filtering kernel, we prove for a second-order CT-$ΣΔ$ that the error estimate may be in $o(1/N^2)$, where $N$ is the oversampling ratio. The whole theory is validated by numerical experiments.
