Identification of System Poles using Hyperbolic Metrics

Alexandros Soumelidis, József Bokor, and Ferenc Schipp


Signals and systems, System identification, Frequency doman representations, Group representations, Hyberbolic geometry


This paper gives an analysis on the opportunities of using some principles of the hyperbolic geometry in the field of signals and systems theory. Based upon the hyperbolic transform realized by the Blaschke function a hyperbolic metric is defined on the unit circle that corresponds to the notions of the Poincare ́ disc model of the hyperbolic geom- etry. Based on the hyperbolic metric and the Laguerre rep- resentation of analytic functions in the unit disc a method is outlined, which gives the opportunity to derive the poles of the functions. Deriving the poles in combination with function representations in rational orthogonal bases solves the nonparametric identification problem in the frequency domain.

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