### 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 Poincaré 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 3rd IASTED Asian Conference on Modelling, Identification, and Control, AsiaMIC 2013 |

Pages | 53-57 |

Number of pages | 5 |

DOIs | |

Publication status | Published - 2013 |

Event | 3rd IASTED Asian Conference on Modelling, Identification, and Control, AsiaMIC 2013 - Phuket, Thailand Duration: Apr 10 2013 → Apr 12 2013 |

### Other

Other | 3rd IASTED Asian Conference on Modelling, Identification, and Control, AsiaMIC 2013 |
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Country | Thailand |

City | Phuket |

Period | 4/10/13 → 4/12/13 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Computer Science Applications
- Software
- Modelling and Simulation

### Cite this

*Proceedings of the 3rd IASTED Asian Conference on Modelling, Identification, and Control, AsiaMIC 2013*(pp. 53-57) https://doi.org/10.2316/P.2013.799-052

**Identification of system poles using hyperbolic metrics.** / Soumelidis, Alexandros; Bokor, J.; Schipp, Ferenc.

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

*Proceedings of the 3rd IASTED Asian Conference on Modelling, Identification, and Control, AsiaMIC 2013.*pp. 53-57, 3rd IASTED Asian Conference on Modelling, Identification, and Control, AsiaMIC 2013, Phuket, Thailand, 4/10/13. https://doi.org/10.2316/P.2013.799-052

}

TY - GEN

T1 - Identification of system poles using hyperbolic metrics

AU - Soumelidis, Alexandros

AU - Bokor, J.

AU - Schipp, Ferenc

PY - 2013

Y1 - 2013

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 Poincaré 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 Poincaré 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=84879847323&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84879847323&partnerID=8YFLogxK

U2 - 10.2316/P.2013.799-052

DO - 10.2316/P.2013.799-052

M3 - Conference contribution

AN - SCOPUS:84879847323

SN - 9780889869462

SP - 53

EP - 57

BT - Proceedings of the 3rd IASTED Asian Conference on Modelling, Identification, and Control, AsiaMIC 2013

ER -