### Abstract

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 geometry. Based on the hyperbolic metric and the Laguerre representation 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.

Original language | English |
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Title of host publication | Proceedings of the IASTED International Conference on Control and Applications, CA 2012 |

Pages | 161-168 |

Number of pages | 8 |

DOIs | |

Publication status | Published - 2012 |

Event | IASTED International Conference on Control and Applications, CA 2012 - Crete, Greece Duration: Jun 18 2012 → Jun 20 2012 |

### Other

Other | IASTED International Conference on Control and Applications, CA 2012 |
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Country | Greece |

City | Crete |

Period | 6/18/12 → 6/20/12 |

### Fingerprint

### Keywords

- Frequency domain representations
- Group representations
- Hyperbolic geometry
- Signals and systems
- System identification

### ASJC Scopus subject areas

- Control and Systems Engineering

### Cite this

*Proceedings of the IASTED International Conference on Control and Applications, CA 2012*(pp. 161-168) https://doi.org/10.2316/P.2012.781-058

**Modeling and identification in frequency domain with representations on the Blaschke group.** / Soumelidis, Alexandras; Bokor, J.; Schipp, Ferenc.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the IASTED International Conference on Control and Applications, CA 2012.*pp. 161-168, IASTED International Conference on Control and Applications, CA 2012, Crete, Greece, 6/18/12. https://doi.org/10.2316/P.2012.781-058

}

TY - GEN

T1 - Modeling and identification in frequency domain with representations on the Blaschke group

AU - Soumelidis, Alexandras

AU - Bokor, J.

AU - Schipp, Ferenc

PY - 2012

Y1 - 2012

N2 - 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 geometry. Based on the hyperbolic metric and the Laguerre representation 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.

AB - 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 geometry. Based on the hyperbolic metric and the Laguerre representation 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.

KW - Frequency domain representations

KW - Group representations

KW - Hyperbolic geometry

KW - Signals and systems

KW - System identification

UR - http://www.scopus.com/inward/record.url?scp=84864754122&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84864754122&partnerID=8YFLogxK

U2 - 10.2316/P.2012.781-058

DO - 10.2316/P.2012.781-058

M3 - Conference contribution

SN - 9780889869226

SP - 161

EP - 168

BT - Proceedings of the IASTED International Conference on Control and Applications, CA 2012

ER -