Abstract
In this paper we consider the problem of approximating a given rational function, where A is a stable (in discrete time sense) matrix. We would like to approximate K(z) with another rational function of the same type, where F is again a stable matrix, but under the restriction that G(z) has fixed number of poles inside the unit circle. Since using the results of Glover [11] we can always find another rational function, where exists and stable, in such a way that is an all-pass transfer function, i.e. and Φ (z) is unitary on the unit circle, so in this paper we examine the approximations of type K(z) — σ Φ(z).
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This paper was partly written while the author was visiting the Statistics and Applied Probability Program, University of California, Santa Barbara.
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© 1992 Springer Science+Business Media Dordrecht
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Michaletzky, G. (1992). Construction of Optimal Hankel Approximations in the Guise of Stochastic Processes. In: Galambos, J., Kátai, I. (eds) Probability Theory and Applications. Mathematics and Its Applications, vol 80. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2817-9_4
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DOI: https://doi.org/10.1007/978-94-011-2817-9_4
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