## Spectral Theory For Random Closed Sets And Estimating The Covariance Via Frequency Space

- A spectral theory for stationary random closed sets is developed and provided with a sound mathematical basis. Definition and proof of existence of the Bartlett spectrum of a stationary random closed set as well as the proof of a Wiener-Khintchine theorem for the power spectrum are used to two ends: First, well known second order characteristics like the covariance can be estimated faster than usual via frequency space. Second, the Bartlett spectrum and the power spectrum can be used as second order characteristics in frequency space. Examples show, that in some cases information about the random closed set is easier to obtain from these characteristics in frequency space than from their real world counterparts.

Author: | K. Koch, J. Ohser, K. Schladitz |
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URN (permanent link): | urn:nbn:de:hbz:386-kluedo-12998 |

Serie (Series number): | Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (37) |

Document Type: | Report |

Language of publication: | English |

Year of Completion: | 2002 |

Year of Publication: | 2002 |

Publishing Institute: | Fraunhofer-Institut für Techno- und Wirtschaftsmathematik |

Date of the Publication (Server): | 2004/02/02 |

Tag: | Bartlett spectrum; Random set; fast Fourier transform; power spectrum |

Faculties / Organisational entities: | Fraunhofer (ITWM) |

DDC-Cassification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |

Licence (German): | Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011 |