.svg){kind=logo}
SPECTRAL ELEMENTS ASSOCIATED TO A CYCLOSTATIONARY FUNCTION
Keywords:
cyclostationarity, random measures, spectral measures, stationary processes, unitary operatorsDOI:
https://doi.org/10.17654/0972086322015Abstract
A cyclostationary function specifies and extends the usual definition of a periodically correlated process. In this paper, we show that with any cyclostationary random function, a unique spectral measure can be associated. With a supplementary continuity hypothesis, we can also associate a unique stationary series. This is a way to consider for such a function the Principal Components Analysis in the frequency domain.
Received: July 27, 2022
Accepted: September 25, 2022
References
R. Azencott and D. Dacunha-Castelle, Séries d’observations irrégulières, Masson, Paris, 1984.
F. Bonardot and M. El Badaoui, Etude de la fatigue d’un coureur, de l’instrumentation à l’analyse vibratoire, Actes du 10e Congrès Français d’Acoustique, Lyon, 12-16 avril 2010, 2010.
https://hal.archives-ouvertes.fr/hal-00537182.
A. Boudou, Groupe d’opérateurs unitaires déduit d’une mesure spectrale - une application, C. R. Acad. Sci. Paris, Série I, Math. 344(12) (2007), 791-794. https://doi.org/10.1016/j.crma.2007.05.013.
A. Boudou and J. Dauxois, Principal component analysis for a stationary random function defined on a locally compact abelian group, J. Multivariate Anal. 51(1) (1994), 1-16. https://doi.org/10.1006/jmva.1994.1046.
A. Boudou and Y. Romain, On spectral and random measures associated with continuous and discrete time processes, Statist. Probab. Lett. 59 (2002), 145-157. https://doi.org/10.1016/S0167-7152(02)00142-6.
A. Boudou and Y. Romain, On product measures associated with stationary processes, The Oxford Handbook of Functional Data Analysis, Oxford Univ. Press, Oxford, 2011, pp. 423-451.
https://doi.org/10.1093/oxfordhb/9780199568444.001.0001.
A. Boudou and S. Viguier-Pla, Principal components analysis and cyclostationarity, J. Multivariate Anal. 189 (2022), 104875.
https://doi.org/10.1016/j.jmva.2021.104875.
G. Bouleux, M. Dugast and F. Macron, Information topological characterization of periodically correlated processes by dilation operators, IEEE Trans. Inform. Theory 65(10) (2019), 6484-6495. https://doi.org/10.1109/TIT.2019.2923217.
E. N. Cabral, Etude spectrale de processus stationnaires multidimensionnels et Analyse en Composantes Principales dans le domaine des frequencies, Doctorat de l’Université Paul Sabatier, Toulouse, France, 2010.
D. Dehay, H. Hurd and A. Makagon, Spectrum of periodically correlated fields, Eur. J. Pure Appl. Math. 7(3) (2014), 343-368.
Retrieved from https://www.ejpam.com/index.php/ejpam/article/view/1995.
J. Dieudonné, Eléments d’analyse, Vol. 6, Gauthier-Villars, Paris, 1975.
M. Ghozzi, Détection cyclostationnaire des bandes de fréquences libres, Doctorat de l’Université de Rennes I, 2008.
P. Gournay, Détection, goniométrie et identification de signaux cyclostationnaires, Doctorat de l’Université de Rennes I, France, 1994.
M. Lamraoui, M. Thomas, M. El Badaoui and F. Girardin, Indicators for monitoring chatter in milling based on instantaneous angular speeds, Mechanical Systems and Signal Processing 44(1-2) (2014), 72-85. https://doi.org/10.1016/j.ymssp.2013.05.002.
F. Zakaria, Analyse de la locomotion humaine: exploitation des propriétés de cyclostationnarité des signaux, Ph.D. Thesis, Université Jean Monnet, Saint Étienne, France, 2015.
Downloads
Published
Issue
Section
License
Copyright (c) 2022 Pushpa Publishing House, Prayagraj, India
This work is licensed under a Creative Commons Attribution 4.0 International License.
____________________________
Attribution: Credit Pusha Publishing House as the original publisher, including title and author(s) if applicable.
Non-Commercial Use: For non-commercial purposes only. No commercial activities without explicit permission.
No Derivatives: Modifying or creating derivative works not allowed without written permission.
Contact Pusha Publishing House for more info or permissions.
