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Singular ARMA signals

Picinbono, Bernard and Tourneret, Jean-Yves Singular ARMA signals. (2005) IEEE Transactions on Signal Processing, 5 (2). 499-504. ISSN 1053-587X

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Official URL: http://dx.doi.org/10.1109/TSP.2004.840783


Singular random signals are characterized by the fact that their values at each time are singular random variables, which means that their distribution functions are continuous but with a derivative almost everywhere equal to zero. Such random variables are usually considered as without interest in engineering or signal processing problems. The purpose of this paper is to show that very simple signals can be singular. This is especially the case for autoregressive moving average (ARMA) signals defined by white noise taking only discrete values and filters with poles located in a circle of singularity introduced in this paper. After giving the origin of singularity and analyzing its relationships with fractal properties, various simulations highlighting this structure will be presented.

Item Type:Article
Additional Information:This publication is available at http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78
HAL Id:hal-03600316
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Other partners > Ecole Supérieure d'Electricité - SUPELEC (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Other partners > Université Paris-Sud 11 (FRANCE)
Laboratory name:
Deposited On:16 Sep 2009 06:57

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