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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Michel Fliess 1 ; Cédric Join 2 ; Mamadou Mboup 3 ; Hebertt Sira-Ramírez 4
@article{CRMATH_2004__339_11_821_0,
author = {Michel Fliess and C\'edric Join and Mamadou Mboup and Hebertt Sira-Ram{\'\i}rez},
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},
}
TY - JOUR AU - Michel Fliess AU - Cédric Join AU - Mamadou Mboup AU - Hebertt Sira-Ramírez TI - Compression différentielle de transitoires bruités JO - Comptes Rendus. Mathématique PY - 2004 SP - 821 EP - 826 VL - 339 IS - 11 PB - Elsevier DO - 10.1016/j.crma.2004.10.003 LA - fr ID - CRMATH_2004__339_11_821_0 ER -
Michel Fliess; Cédric Join; Mamadou Mboup; Hebertt Sira-Ramírez. Compression différentielle de transitoires bruités. Comptes Rendus. Mathématique, Volume 339 (2004) no. 11, pp. 821-826. doi : 10.1016/j.crma.2004.10.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.10.003/
[1] Ondelettes, multifractales et turbulences, Diderot, Paris, 1995
[2] A Practical Guide to Splines, Springer, New York, 2001
[3] Algèbre, Masson, Paris, 1981 (chap. 4 à 7)
[4] Theorie und Anwendung der Laplace Transformation, Springer, Berlin, 1937
[5] Temps-fréquence, Hermès, Paris, 1998
[6] An introduction to nonlinear fault diagnosis with an application to a congested internet router (S. Tarbouriech; C. Abdallah; J. Chiasson, eds.), Advances in Communication Control Networks, Lecture Notes in Control and Inform. Sci., vol. 308, Springer, Londres, 2004
[7] Questioning some paradigms of signal processing via concrete examples (H. Sira-Ramírez; G. Silva-Navarro, eds.), Algebraic Methods in Flatness, Signal Processing and State Estimation, Editiorial Lagares, México, 2003, pp. 1-21
[8] An algebraic framework for linear identification, ESAIM Control Optim. Calc. Var., Volume 9 (2003), pp. 151-168
[9] Reconstructeurs d'états, C. R. Acad. Sci. Paris, Ser. I, Volume 338 (2004), pp. 91-96
[10] Control via state estimations of some nonlinear systems, Proc. NOLCOS, Stuttgart, 2004
[11] Vector Quantization and Signal Compression, Kluwer Academic, Boston, 1992
[12] An Introduction to Differential Algebra, Hermann, Paris, 1976
[13] Differential Algebra and Algebraic Groups, Academic Press, New York, 1973
[14] Une exploration des signaux en ondelettes, Éditions École Polytechnique, Palaiseau, 2000
[15] Noncommutative Noetherian Rings, Amer. Math. Society, Providence, RI, 2000
[16] Operational Calculus, vol. 1, PWN, Varsovie & Oxford University Press, Oxford, 1983
[17] Operational Calculus, vol. 2, PWN, Varsovie & Oxford University Press, Oxford, 1987
[18] Techniques de compression des signaux, Masson, Paris, 1995
[19] Introduction to Data Compression, Morgan Kaufmann, San Francisco, 2000
[20] Operational Calculus, Springer, New York, 1984
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