The use of second-order information in the approximation of discreate-time linear systems
The use of second-order information in the approximation of discreate-time linear systems
复制标题
二阶信息在离散时间线性系统逼近中的应用
DOI：
10.1109/tassp.1976.1162795
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发表时间：
1976
期刊：
影响因子：
--
通讯作者：
R. Roberts
中科院分区：
文献类型：
--
作者：
C. Mullis;R. Roberts
通常的做法是用其脉冲响应的有限部分来描述滤波器的部分特征，目的是产生递归近似。本文讨论了以脉冲响应和自相关序列的有限部分的形式混合第一和第二信息的使用。本文讨论了用于此目的的许多技术和算法。研究了两个逼近问题：一个插值法问题和一个最小二乘问题。这些都被证明是密切相关的。构成这些问题解的线性系统被证明是稳定的。给出了一种有效的求解算法，并证明了该算法与著名的Levinson算法和Jury稳定性检验密切相关。这些算法之间的紧密联系表明它们在稳定离散线性系统的数值分析中是基本的。
It is common practice to partially characterize a filter with a finite portion of its impulse response, with the objective of generating a recursive approximation. This paper discusses the use of mixed first and second information, in the form of a finite portion of the impulse response and autocorrelation sequences. The discussion encompasses a number of techniques and algorithms for this purpose. Two approximation problems are studied: an interpolation problem and a least squares problem. These are shown to be closely related. The linear systems which form the solutions to these problems are shown to be stable. An efficient algorithm for obtaining solutions is given and shown to be closely related to a well-known algorithm of Levinson and the Jury stability test. The close connection between these algorithms suggests that they are fundamental in the numerical analysis of stable discrete-time linear systems.