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Multiscale signal processing : isotropic random fields on homogeneous trees

Bernhard Claus 1 Ghislaine Chartier 1
1 AS - Signal Processing and Control
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, INRIA Rennes
Abstract : In this paper we consider isotropic processes on a homogeneous tree of order q, i.e. stochastic processes which covariance function depends only on the distance on the tree. We develop a characterization of isotropic processes via a reflection coefficient sequence. The relation between the covariance sequence and the reflection coefficient sequence of a process is derived by generalized Levinson and Schur recursions respectively . Although these results are easily obtained using an isometric (i.e. non-oriented) approach, the Levinson and Schur recursions are also given from the pyramidal point of view. They turn out to be useful in this form for the implementation of generating and whitening filters.
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https://hal.inria.fr/inria-00076946
Contributor : Rapport de Recherche Inria <>
Submitted on : Monday, May 29, 2006 - 11:39:42 AM
Last modification on : Thursday, February 11, 2021 - 2:48:07 PM
Long-term archiving on: : Friday, May 13, 2011 - 10:10:24 PM

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  • HAL Id : inria-00076946, version 1

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Bernhard Claus, Ghislaine Chartier. Multiscale signal processing : isotropic random fields on homogeneous trees. [Research Report] RR-1709, INRIA. 1992. ⟨inria-00076946⟩

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