Approximation and realization using generalized orthonormal bases

P. Heuberger, T. Hoog, P. V. D. Hof
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Abstract

This paper considers the approximation of linear systems by means of orthonormal basis functions, which are generated by stable all-pass functions. These basis functions induce the so called Hambo transform, which transforms scalar systems into square systems of i/o dimension equal to the order of the all-pass function considered. We will consider the construction of the Markov parameters of the system representation in the transform domain and show how these can be used to realize minimal state space representations for the exact and partial knowledge case. Additionally a projection mechanism is presented to allow inverse transformation of any sequence of Markov parameters in the transform domain. This mechanism is illustrated with an example.
用广义标准正交基逼近和实现
研究了用稳定全通函数生成的正交基函数逼近线性系统的问题。这些基函数引出了所谓的Hambo变换,它将标量系统转换成与所考虑的全通函数的阶数相等的i/o维的平方系统。我们将考虑在变换域中系统表示的马尔可夫参数的构造,并展示如何使用这些参数来实现精确和部分知识情况下的最小状态空间表示。此外,还提出了一种投影机制,允许在变换域中对任意马尔可夫参数序列进行逆变换。通过一个例子说明了这种机制。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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