Critique du rapport signal à bruit en communications numériques

Michel Fliess

doi:10.46298/arima.1908

Michel Fliess - Questioning the signal to noise ratioin digital communications

arima:1908 - Revue Africaine de Recherche en Informatique et Mathématiques Appliquées, October 22, 2008, Volume 9, 2007 Conference in Honor of Claude Lobry, 2008 - https://doi.org/10.46298/arima.1908

Questioning the signal to noise ratioin digital communicationsArticle

Authors: Michel Fliess ^1,²

1 Algebra for Digital Identification and Estimation [LIX]
2 Laboratoire d'informatique de l'École polytechnique [Palaiseau]

The signal to noise ratio, which plays such an important rôle in information theory, is shown to become pointless for digital communications where the demodulation is achieved via new fast estimation techniques. Operational calculus, differential algebra, noncommutative algebra and nonstandard analysis are the main mathematical tools.

https://doi.org/10.46298/arima.1908

Source: HAL:inria-00311719v4

Volume: Volume 9, 2007 Conference in Honor of Claude Lobry, 2008

Published on: October 22, 2008

Submitted on: April 17, 2008

Keywords: noncommutative algebra, nonstandard analysis., differential algebra, operational calculus, estimation, signal to noise ratio, noises, demodulation, modulation, symbols, carriers, signal processing, digital communications,Information theory,porteuses,symboles,modulation,démodulation,bruits,estimation,rapport signal à bruit,calcul opérationnel,algèbre différentielle,algèbre non commutative,analyse non standard,Théorie de l’information,traitement du signal,communications numériques,[INFO] Computer Science [cs],[MATH] Mathematics [math]

Bibliographic References

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Da-yan Liu;Olivier Gibaru;Wilfrid Perruquetti, arXiv (Cornell University), Convergence Rate of the Causal Jacobi Derivative Estimator, pp. 445-455, 2012, 10.1007/978-3-642-27413-8_28, https://arxiv.org/abs/1106.2208.

Da-Yan Liu;Olivier Gibaru;Wilfrid Perruquetti, 2011, Error analysis of Jacobi derivative estimators for noisy signals, 58, 1, pp. 53-83, 10.1007/s11075-011-9447-8, https://hal.inria.fr/inria-00573270/file/finale_corrige_V1.pdf.

Da-yan Liu;Olivier Gibaru;Wilfrid Perruquetti, 2010, Differentiation by integration with Jacobi polynomials, Journal of Computational and Applied Mathematics, 235, 9, pp. 3015-3032, 10.1016/j.cam.2010.12.023, https://doi.org/10.1016/j.cam.2010.12.023.

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