Deterministic analysis of oversampled A/D conversion and decoding improvement based on consistent estimates
Deterministic analysis of oversampled A/D conversion and decoding improvement based on consistent estimates
复制标题
基于一致估计的过采样 A/D 转换和解码改进的确定性分析
DOI：
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发表时间：
1994
影响因子：
5.4
通讯作者：
M. Vetterli
中科院分区：
文献类型：
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作者：
N. T. Thao;M. Vetterli
讨论了过采样A/D转换（ADC）的确定性分析，从这样的分析推导出的属性，以及使用非线性解码重建的后果。给定带限输入X产生量化版本C，作者考虑所有带限输入信号的集合并产生C。他们称这个集合的任何元素都是X的一致估计。无论编码器的类型（简单、预测或噪声整形）如何，它们都表明该集合是凸的，因此，任何不一致的估计都可以得到改善。他们还表明，经典的线性解码估计不一定是一致的。对简单ADC、单环路和多环路/spl Sigma//spl Delta/调制进行的数值测试表明，一致的估计产生的均方误差（MSE）随着过采样率渐近下降，比线性解码MSE快约3 dB/倍频程。这意味着线性解码中的渐近MSE为/spl Oscr/（R/sup /spl minus/（2n+2/））而不是/spl Oscr/（R/sup /spl minus/（2n+1/）），其中R是过采样率，n是调制器的阶数。提出了基于量化信号的确定性知识的非一致估计的改进方法，用于简单ADC、预测ADC、单环和多环/spl Sigma//spl Delta/调制。>
Discusses the deterministic analysis of oversampled A/D conversion (ADC), the properties derivable from such an analysis, and the consequences on reconstruction using nonlinear decoding. Given a band-limited input X producing a quantized version C, the authors consider the set of all input signals that are band-limited and produce C. They call any element of this set a consistent estimate of X. Regardless of the type of encoder (simple, predictive, or noise-shaping), they show that this set is convex, and as a consequence, any nonconsistent estimate can be improved. They also show that the classical linear decoding estimates are not necessarily consistent. Numerical tests performed on simple ADC, single-loop, and multiloop /spl Sigma//spl Delta/ modulation show that consistent estimates yield a mean square error (MSE) that decreases asymptotically with the oversampling ratio faster than the linear decoding MSE by approximately 3 dB/octave. This implies an asymptotic MSE of the order of /spl Oscr/(R/sup /spl minus/(2n+2/)) instead of /spl Oscr/(R/sup /spl minus/(2n+1/)) in linear decoding, where R is the oversampling ratio and n the order of the modulator. Methods of improvement of nonconsistent estimates based on the deterministic knowledge of the quantized signal are proposed for simple ADC, predictive ADC, single-loop, and multiloop /spl Sigma//spl Delta/ modulation. >