Algèbre différentielle, algèbre non commutative et calcul opérationnel conduisent à des méthodes efficaces et simples d'analyse et de compression de signaux transitoires bruités. Deux exemples, l'un académique, l'autre musical, illustrent notre propos.
The analysis and compression of noisy transient signals are handled via methods stemming from elementary differential algebra, noncommutative algebra and operational calculus. The efficiency of our approach is illustrated by an academic example and a more concrete case-study which is a musical signal.
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@article{CRMATH_2004__339_11_821_0,
author = {Fliess, Michel and Join, C\'edric and Mboup, Mamadou and Sira-Ram{\'\i}rez, Hebertt},
title = {Compression diff\'erentielle de transitoires bruit\'es},
journal = {Comptes Rendus. Math\'ematique},
pages = {821--826},
publisher = {Elsevier},
volume = {339},
number = {11},
year = {2004},
doi = {10.1016/j.crma.2004.10.003},
language = {fr},
url = {http://archive.numdam.org/articles/10.1016/j.crma.2004.10.003/}
}
TY - JOUR AU - Fliess, Michel AU - Join, Cédric AU - Mboup, Mamadou AU - Sira-Ramírez, Hebertt TI - Compression différentielle de transitoires bruités JO - Comptes Rendus. Mathématique PY - 2004 SP - 821 EP - 826 VL - 339 IS - 11 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2004.10.003/ DO - 10.1016/j.crma.2004.10.003 LA - fr ID - CRMATH_2004__339_11_821_0 ER -
%0 Journal Article %A Fliess, Michel %A Join, Cédric %A Mboup, Mamadou %A Sira-Ramírez, Hebertt %T Compression différentielle de transitoires bruités %J Comptes Rendus. Mathématique %D 2004 %P 821-826 %V 339 %N 11 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2004.10.003/ %R 10.1016/j.crma.2004.10.003 %G fr %F CRMATH_2004__339_11_821_0
Fliess, Michel; Join, Cédric; Mboup, Mamadou; Sira-Ramírez, Hebertt. Compression différentielle de transitoires bruités. Comptes Rendus. Mathématique, Tome 339 (2004) no. 11, pp. 821-826. doi : 10.1016/j.crma.2004.10.003. http://archive.numdam.org/articles/10.1016/j.crma.2004.10.003/
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