A unified approach to the optimal synthesis of fixed-point state-space digital filters
A unified approach to the optimal synthesis of fixed-point state-space digital filters
复制标题
定点状态空间数字滤波器最优综合的统一方法
DOI：
10.1109/tassp.1985.1164638
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发表时间：
1985
期刊：
影响因子：
--
通讯作者：
T. Higuchi
中科院分区：
文献类型：
--
作者：
M. Kawamata;T. Higuchi
本文提出了定点型状态空间数字滤波器因系数量化而产生的输出误差方差在时间域中的两个表达式。一种是确定性方法，它精确地给出了状态空间数字滤波器的输出误差方差。另一种是统计方法，将系数量化的误差假设为独立的随机变量。该统计方法为分析状态空间数字滤波器因系数量化而产生的输出误差方差提供了一种简单易行的方法。由统计方法引入的统计系数灵敏度与四舍五入噪声功率增益等价。因此，对于系数灵敏度和舍入噪声而言都是最优的状态空间数字滤波器可以通过舍入噪声最小化的方法来综合。这种可以是任意阶次的最优状态空间数字滤波器被证明是没有自主溢出极限环的。给出了一个数值算例，说明了系数量化输出误差方差分析和综合方法的有效性。
This paper proposes two expressions of the output error variance due to coefficient quantization of fixed-point state-space digital filters in the time domain. One is the deterministic approach, which gives precisely the output error variance of state-space digital filters. The other is the statistical approach, where the errors of coefficient quantization are assumed to be independent random variables. The statistical approach gives a simple and easy way to analyze the output error variance due to coefficient quantization of state-space digital filters. The statistical coefficient sensitivity introduced by the statistical approach is shown to be equivalent to the round off noise power gain. Thus, state-space digital filters which are optimal with respect to both coefficient sensitivity and roundoff noise can be synthesized by the method of minimization of the roundoff noise. Such optimal state-space digital filters which could be of any order are proved to be free of autonomous overflow limit cycles. A numerical example is given to illustrate the effectiveness of the analysis of the output error variance due to coefficient quantization and the synthesis method proposed here.