transpacours6 - Ph Loubaton Notions sur les signaux...

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Ph. Loubaton Notions sur les signaux al´ eatoires. Fili` ere R´ eseau 1/21
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Ph. Loubaton Introduction Signaux dont on ne peut connaitre les valeurs avant des les avoir observ´ es : impr´ evisibles. Mise en ´ evidence de techniques permettant d’´ evaluer des propri´ et´ es statistiques (i.e. moyennes) pour en avoir une meilleure connaissance quantitative. Exemples. Le bruit de fond b ( t ) Signal x ( t ) = n Z a n g ( t - nT ) transmis par un syst` eme de communication : la suite ( a n ) n Z est al´ eatoire. Question typique relative aux notions qui vont ˆ etre introduites : Quelle bande passante r´ eserver a priori ` a la transmission du signal x ( t ) = n Z a n g ( t - nT ) ? D´ efinir un concept de bande passante moyenne. Fili` ere R´ eseau 2/21
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Ph. Loubaton Trajectoires d’un signal al´ eatoire I. Variable al´ eatoire x = nombre r´ eel dont la valeur est impr´ evisible avant de l’observer lors d’une exp´ erience ealisation de x = valeur prise par x lors d’une exp´ erience. Signal al´ eatoire x ( t ) = signal dont tel que pour tout t , x ( t ) est une variable al´ eatoire. ealisation d’un signal al´ eatoire x ( t ) = ensemble des valeurs prises par les v.a. x ( t ) quand t varie. Appel´ e aussi trajectoire. Fili` ere R´ eseau 3/21
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Ph. Loubaton Trajectoires d’un signal al´ eatoire II. Exemple 1 : n a n g ( t - nT ) 0 50 100 150 200 250 300 350 400 -1.5 -1 -0.5 0 0.5 1 1.5 Fili` ere R´ eseau 4/21
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Ph. Loubaton Trajectoires d’un signal al´ eatoire III. Exemple 2 : bruit de fond . 0 50 100 150 200 250 300 350 400 -3 -2 -1 0 1 2 3 Fili` ere R´ eseau 5/21
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Ph. Loubaton Trajectoires d’un signal al´ eatoire IV. Exemple 3 : bruit de fond filtre . 0 50 100 150 200 250 300 350 400 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Fili` ere R´ eseau 6/21
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Ph. Loubaton Trajectoires d’un signal al´ eatoire V.
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