Mean Squared Error Analysis of Quantizers With Error Feedback
Mean Squared Error Analysis of Quantizers With Error Feedback
复制标题
带误差反馈的量化器的均方误差分析
DOI：
10.1109/tsp.2017.2745450
复制
发表时间：
2017
影响因子：
5.4
通讯作者：
Nagahara Masaaki
中科院分区：
文献类型：
--
作者：
Ohno Shuichi;Shiraki Teruyuki;Tariq M. Rizwan;Nagahara Masaaki
量化是数字信号处理中的一个基本过程。ΔΣ调制器经常用于量化，这可以很容易地用静态均匀量化器和误差反馈滤波器来实现。本文分析了包括ΔΣ调制器在内的误差反馈量化器的均方量化误差。首先，我们研究了具有使量化均方误差(MSE)最小化的理想最优误差反馈滤波器的量化器。我们证明了最优误差反馈滤波器的幅值响应可以用一个参数来参数化。这种参数化使我们能够从数值上找到最优的误差反馈滤波器。其次，通过使用最优误差反馈滤波器，阐明了用于量化器的比特数与可实现的均方误差之间的关系。这使得可以根据均方误差来考察具有最佳误差反馈滤波器的量化器的效率。然后，利用Yule-Walker方法和基于线性矩阵不等式的方法，用实际可实现的滤波器逼近理想的最优误差反馈滤波器。文中给出了数值算例，以演示我们的分析和综合。
Quantization is a fundamental process in digital signal processing. ΔΣ modulators are often utilized for quantization, which can be easily implemented with static uniform quantizers and error feedback filters. In this paper, we analyze the mean squared quantization error of the quantizer with error feedback including the ΔΣ modulators. First, we study the quantizer with an ideal optimal error feedback filter that minimizes the mean squared error (MSE) of quantization. We show that the amplitude response of the optimal error feedback filter can be parameterized by one parameter. This parameterization enables us to find the optimal error feedback filter numerically. Second, the relationship between the number of bits used for the quantizer and the achievable MSE is clarified by using the optimal error feedback filter. This makes it possible to investigate the efficiency of the quantizer with the optimal error feedback filter in terms of MSE. Then, ideal optimal error feedback filters are approximated by practically implementable filters using the Yule-Walker method and the linear matrix inequality-based method. Numerical examples are provided for demonstrating our analysis and synthesis.