Critique du rapport signal à bruit en communications numériques -- Questioning the signal to noise ratio in digital communications

The signal to noise ratio, which plays such an important r\^ole 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.

[1]  M. Fliess,et al.  Compression différentielle de transitoires bruités , 2004 .

[2]  Masoud Salehi,et al.  Communication Systems Engineering , 1994 .

[3]  Salvatore Tabbone,et al.  Robust Curvature Extrema Detection Based on New Numerical Derivation , 2008, ACIVS.

[4]  Richard E. Blahut,et al.  Principles and practice of information theory , 1987 .

[5]  S. Albeverio.  Nonstandard Methods in Stochastic Analysis and Mathematical Physics , 1986 .

[6]  Michel Fliess,et al.  Analyse non standard du bruit , 2006, ArXiv.

[7]  吉田 耕作.  Operational calculus: A theory of hyperfunctions , 1984 .

[8]  Dayan Liu,et al.  An error analysis in the algebraic estimation of a noisy sinusoidal signal , 2008, 2008 16th Mediterranean Conference on Control and Automation.

[9]  Michel Fliess.  Critique du rapport signal à bruit en théorie de l'information -- A critical appraisal of the signal to noise ratio in information theory , 2007, ArXiv.

[10]  Cédric Join,et al.  Numerical differentiation with annihilators in noisy environment , 2009, Numerical Algorithms.

[11]  C.E. Shannon,et al.  Communication in the Presence of Noise , 1949, Proceedings of the IRE.

[12]  Vicente Feliú Batlle,et al.  On the algebraic identification of the frequencies, amplitudes and phases of two sinusoidal signals from their noisy sum , 2008, Int. J. Control.

[13]  Cédric Join,et al.  Time Series Technical Analysis via New Fast Estimation Methods: A Preliminary Study in Mathematical Finance , 2008 .

[14]  Hebertt Sira-Ramírez,et al.  Closed-loop parametric identification for continuous-time linear systems via new algebraic techniques , 2007 .

[15]  L. Brillouin,et al.  Science and information theory , 1956 .

[16]  K. Yosida.  Operational Calculus: A Theory of Hyperfunctions , 1984 .

[17]  M. Fliess,et al.  Commande sans modèle et commande à modèle restreint , 2008 .

[18]  A. Zeilinger,et al.  Conceptual inadequacy of the Shannon information in quantum measurements , 2000, quant-ph/0006087.

[19]  Mamadou Mboup,et al.  Parameter estimation via differential algebra and operational culculus , 2007 .

[20]  Kurt Schlacher,et al.  An introduction to algebraic discrete-time linear parametric identification with a concrete application , 2008 .

[21]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[22]  Michel Fliess,et al.  Probabilités et fluctuations quantiques (Probabilities and quantum fluctuations) , 2007, 0704.2019.

[23]  Cédric Join,et al.  Non-linear estimation is easy , 2007, Int. J. Model. Identif. Control..

[24]  Cédric Join,et al.  Robust residual generation for linear fault diagnosis: an algebraic setting with examples , 2004 .

[25]  Jürgen Potthoff,et al.  White Noise: An Infinite Dimensional Calculus , 1993 .

[26]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[27]  M. Fliess,et al.  Questioning some paradigms of signal processing via concrete examples , 2003 .

[28]  M. Fliess,et al.  An algebraic framework for linear identification , 2003 .

[29]  Vicente Feliú Batlle,et al.  An algebraic frequency estimator for a biased and noisy sinusoidal signal , 2007, Signal Process..

[30]  Alain Robert.  Analyse non standard , 1985 .

[31]  Tewfik Sari,et al.  Non-standard analysis and representation of reality , 2008, Int. J. Control.

[32]  J. McConnell,et al.  Noncommutative Noetherian Rings , 2001 .

[33]  Maria D. Miranda,et al.  Algebraic parameter estimation of damped exponentials , 2007, 2007 15th European Signal Processing Conference.

[34]  Cédric Join,et al.  A delay estimation approach to change-point detection , 2007 .

[35]  H. S. Green.  Information Theory and Quantum Physics , 2000 .

[36]  M. Fliess,et al.  Reconstructeurs d'état , 2004 .

[37]  R. Charreton.  Une loi limite pour les marches aléatoires avec des applications physiques , 2007 .

[38]  Denyse Baillargeon,et al.  Bibliographie , 1929 .

[39]  H. Sira-Ramírez,et al.  A fast on-line frequency estimator of lightly damped vibrations in flexible structures , 2007 .

[40]  Michel Fliess.  Réflexions sur la question fréquentielle en traitement du signal , 2005, ArXiv.