Digital phase-locked loops tracked by a relay sensor

An optimal algorithm is presented for tracking the phase of a slowly modulating signal by means of digital sampling of its sign. Error bounds and a numerical illustration are given

Solutions to muscle fiber equations and their long time behaviour

We consider the nonlinear initial-boundary value problem governing the dynamical displacements of a one dimensional solid body with specific stress-strain law. This constitutive law results from the modelization of the mechanisms that rules the electrically activated mechanical behaviour of cardiac muscle fibers at the microscopic level. We prove global existence and uniqueness of solutions and we study their asymptotic behaviour in time. In particular we show that under vanishing external forcing solutions asymptotically converge to an equilibrium

Dither in Systems with Hysteresis

Projet SOSSOThis paper deals with differential inclusion containing an hysteresis nonlinearity and two inputs: a control input and a dither input of high frequency. Conditions are introduced under which its solution admits asymptotic behavior when the dither frequency goes to infinity. According to asymptotic growth of the dither amplitude, two different behaviors appear: the nonlinearity is smoothed (resp. quenched) if the velocities induced by the dither are asymptotically bounded (resp. unbo- unded). Convergence results for finite and infinite time intervals are given, and linked with the averaging principle. The case of bounded dithering velocities is of interest in a mechanical context, where hysteresis is used to model dry friction. A very interesting feature is that the averaged hysteresis operator may be linearized for small velocities. The hypotheses on the dither include periodicity, $F$-repetitiveness and (asymptotic) almost-periodicity

SynDEx : un environnement de programmation pour applications de traitement du signal distribuées

On présente une méthode de programmation pour des applications de traitement du signal en temps-réel sur machines multi-processeur. Cette méthode s'appuie sur le langage synchrone SIGNAL pour spécifier et prouver les algorithmes d'application et sur l'environnement de programmation SynDEx pour générer des exécutifs temps-réel distribués optimisés. Cette méthode est appliquée à un exemple d'égalisation adaptative

Multi-scale modeling of the follicle selection process in the ovary

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