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Lower Bound on the Mean-Squared Error in Oversampled Quantization of Periodic Signals Using Vector Quantization Analysis

机译:使用矢量量化分析的周期信号过采样量化中均方误差的下界

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摘要

Oversampled analog-to-digital conversion is a technique which permits high conversion resolution using coarse quantization. Classically, by lowpass filtering the quantized oversampled signal, it is possible to reduce the quantization error power in proportion to the oversampling ratio R. In other words, the reconstruction mean-squared error (MSE) is in (R-1). It was recently found that this error reduction is not optimal. Under certain conditions, it was shown on periodic bandlimited signals that an upper bound on the MSE of optimal reconstruction is in (R-2) instead of (R -1). In the present paper, we prove on the same type of signals that the order (R-2) is the theoretical limit of reconstruction as an MSE lower bound. The proof is based on a vector-quantization approach with an analysis of partition cell density
机译:过采样的模数转换是一种允许使用粗量化实现高转换分辨率的技术。经典地,通过对量化的过采样信号进行低通滤波,可以与过采样率R成比例地减小量化误差功率。换句话说,重建均方误差(MSE)在(R-1)中。最近发现,这种错误减少不是最佳的。在某些条件下,在周期性带限信号上显示,最佳重构的MSE的上限位于(R-2)中,而不是(R -1)中。在本文中,我们证明在相同类型的信号上,阶数(R-2)是作为MSE下限重构的理论极限。该证明基于矢量量化方法,并分析了分区的细胞密度

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