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# Rational Approximation of Transfer Functions in the Hyperion Software

Abstract : The objective of this paper is to explain how rational approximation is performed within the hyperion software. This work is divided into three parts. In the first part, we explain the theory underlying the algorithm: given some Fourier coefficients, find a rational transfer function of McMillan degree $n$ of best approximation in the $l^2$-sense to the correspond- ing Fourier series. This gives a certain number of equations for stationary points and we detail in the second part how they can be efficiently solved numerically, using techniques of automatic differentiation. In the last part, we further discuss the complexity of the implementation thus obtained.
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https://hal.inria.fr/inria-00072642
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Submitted on : Wednesday, May 24, 2006 - 10:29:06 AM
Last modification on : Friday, February 4, 2022 - 3:19:06 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:16:44 PM

### Identifiers

• HAL Id : inria-00072642, version 1

### Citation

José Grimm. Rational Approximation of Transfer Functions in the Hyperion Software. [Research Report] RR-4002, INRIA. 2000, pp.245. ⟨inria-00072642⟩

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