Critique du rapport signal \`a bruit en th\'eorie de l'information -- A critical appraisal of the signal to noise ratio in information theory

Abstract

The signal to noise ratio, which plays such an important role in information theory, is shown to become pointless in digital communications where - symbols are modulating carriers, which are solutions of linear differential equations with polynomial coefficients, - demodulations is achieved thanks to new algebraic estimation techniques. Operational calculus, differential algebra and nonstandard analysis are the main mathematical tools.