Orthonormal Basis Functions in Time and Frequency Domain: Hambo Transform Theory
Orthonormal Basis Functions in Time and Frequency Domain: Hambo Transform Theory
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时域和频域中的正交基函数：Hambo 变换理论
DOI：
10.1137/s0363012902405340
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
B. Wahlberg
中科院分区：
文献类型：
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作者：
P. Heuberger;T. Hoog;P. V. D. Hof;B. Wahlberg
有限脉冲响应（FIR）函数、Laguerre函数和考茨函数类可以推广到稳定线性动力系统的哈代空间H2上的有理正交基函数族。这些基函数对于构造线性系统和信号的有效参数化和编码是有用的，例如，系统辨识、系统逼近和自适应滤波。在本文中，基函数来自传递函数的角度来看，以及在状态空间设置。它示出了这种方法如何导致系统和信号在时域和频域中的替代系列扩展。广义基函数诱导信号和系统变换（Hambo变换），这已被证明是有用的分析工具，在各种建模问题。本文对这些变换进行了详细的分析，并导出了它们的大量性质。原则上，它示出了如何最小的状态空间实现的系统变换可以从原始系统的最小状态空间实现，反之亦然。
The class of finite impulse response (FIR), Laguerre, and Kautz functions can be generalized to a family of rational orthonormal basis functions for the Hardy space H2 of stable linear dynamical systems. These basis functions are useful for constructing efficient parameterizations and coding of linear systems and signals, as required in, e.g., system identification, system approximation, and adaptive filtering. In this paper, the basis functions are derived from a transfer function perspective as well as in a state space setting. It is shown how this approach leads to alternative series expansions of systems and signals in time and frequency domain. The generalized basis functions induce signal and system transforms (Hambo transforms), which have proved to be useful analysis tools in various modelling problems. These transforms are analyzed in detail in this paper, and a large number of their properties are derived. Principally, it is shown how minimal state space realizations of the system transform can be obtained from minimal state space realizations of the original system and vice versa.