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Title:Approximating arbitrary impulse response functions with Prony basis functions
Author(s):Herber, Daniel Ronald; Allison, James T.
Subject(s):convolution integral
impulse response
state-space model
transfer function
Abstract:In this report, we are concerned with approximating the input-to-output behavior of a type of scalar convolution integral given its so-called impulse response function by constructing an appropriate linear time-invariant state-space model. Such integrals frequently appear in the modeling of hydrodynamic forces, viscoelastic materials, among other applications. First, linear systems theory is reviewed. Next, Prony basis functions, which are exponentially decaying cosine waves with phase delay and variable amplitude, are described as potential objects to be used to approximate a given impulse response function. Then it is shown how a superposition of Prony basis functions can be directly mapped back to an equivalent linear state-space model. Also, it is directly shown that both the Golla-Hughes-McTavish model and Prony series (generalized Maxwell model) are special cases of the considered Prony basis function. Several nonlinear optimization (fitting) problems are then described to determine the value of the model parameters that result in the desired approximation. Finally, a few numerical examples are presented to demonstrate that Prony basis functions can approximation a diverse set of impulse response behaviors.
Issue Date:2019-10-21
Citation Info:Daniel R Herber and James T Allison. ‘Approximating arbitrary impulse response functions with Prony basis functions.’ Technical Report UIUC-ESDL-2019-01, Oct. 2019.
Genre:Technical Report
Rights Information:Copyright 2019 Daniel R. Herber
Date Available in IDEALS:2019-12-13

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