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Catégorie :Category: nCreator TI-Nspire
Auteur Author: mauricinho
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 2.38 Ko KB
Mis en ligne Uploaded: 10/07/2025 - 04:05:54
Uploadeur Uploader: mauricinho (Profil)
Téléchargements Downloads: 3
Visibilité Visibility: Archive publique
Shortlink : https://tipla.net/a4790780
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 2.38 Ko KB
Mis en ligne Uploaded: 10/07/2025 - 04:05:54
Uploadeur Uploader: mauricinho (Profil)
Téléchargements Downloads: 3
Visibilité Visibility: Archive publique
Shortlink : https://tipla.net/a4790780
Description
Fichier Nspire généré sur TI-Planet.org.
Compatible OS 3.0 et ultérieurs.
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=Ì ENTROPÍA AYUDANTÍA COMUNICACIONES <¯ Def: H(X) = (pb·log(pb)) H(X,Y) = (p(x,y)·log(p(x,y))) H(Y|X) = (p(x,y)·log(p(y|x))) I(X;Y) = H(Y)H(Y|X) =á EJ1: CANAL TERNARIO P(X=0)=0.5 ; P(X=1)=0.3 ; P(X=2)=0.2 =Ê P(Y|X) = [0.8 0.15 0.05 0.1 0.7 0.2 0.05 0.25 0.7] H(X) = [0.5·log(0.5) + 0.3·log(0.3) + 0.2·log(0.2)] H 1.4855 P(Y): P(Y=0)=0.5·0.8 + 0.3·0.1 + 0.2·0.05 = 0.44 P(Y=1)=0.5·0.15 + 0.3·0.7 + 0.2·0.25 = 0.335 P(Y=2)=0.5·0.05 + 0.3·0.2 + 0.2·0.7 = 0.225 H(Y)=[0.44·log(0.44) + 0.335·log(0.335) + 0.225·log(0.225)] H 1.5334 P(X,Y): P(0,0)=0.4 ; P(0,1)=0.075 ; P(0,2)=0.025 P(1,0)=0.03 ; P(1,1)=0.21 ; P(1,2)=0.06 P(2,0)=0.01 ; P(2,1)=0.05 ; P(2,2)=0.14 H(X,Y)=[P·log(P)] H 2.4898 H(Y|X): H(Y|X=0)=0.8842 ; H(Y|X=1)=1.1568 ; H(Y|X=2)=1.1219 H(Y|X)=0.5·0.8842 + 0.3·1.1568 + 0.2·1.1219 H 1.0135 I(X;Y)=H(Y)H(Y|X)=1.53341.0135=0.5198 Efic=I/H(X)=0.5198/1.4855=35% Capacidad rel=I/log(3)=0.5198/1.585=32.8% =á EJ2: CANAL AWGN B=1e6 ; N=1e-9 ; Pmax=1e-3 ; R=1.5e6 Pn = N·B = 1e-3 SNR = Pmax/Pn = 1 Capacidad: C = B·log(1+SNR) = 1e6·log(2) = 1e6 bps = 1 Mbps R > C No es posible sin errores Opciones: 1) B: Bnuevo = R/log(1+SNR) = 1.5 MHz 2) P: SNRreq=2^1.51=2.828 Ò Preq = 2.828·Pn = 2.828 mW 3) R: Rmáx = C = 1 Mbps Prob error: Eb/N = SNR·B/R = 1e6/1.5e6 = 0.667 Pe = Q((2·0.667)) H Q(1.155) H 0.124 =Ì RECOMENDACIÓN: Inviable con R=1.5 Mbps y B=1 MHz sin potencia o anchoB Made with nCreator - tiplanet.org
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Compatible OS 3.0 et ultérieurs.
<<
=Ì ENTROPÍA AYUDANTÍA COMUNICACIONES <¯ Def: H(X) = (pb·log(pb)) H(X,Y) = (p(x,y)·log(p(x,y))) H(Y|X) = (p(x,y)·log(p(y|x))) I(X;Y) = H(Y)H(Y|X) =á EJ1: CANAL TERNARIO P(X=0)=0.5 ; P(X=1)=0.3 ; P(X=2)=0.2 =Ê P(Y|X) = [0.8 0.15 0.05 0.1 0.7 0.2 0.05 0.25 0.7] H(X) = [0.5·log(0.5) + 0.3·log(0.3) + 0.2·log(0.2)] H 1.4855 P(Y): P(Y=0)=0.5·0.8 + 0.3·0.1 + 0.2·0.05 = 0.44 P(Y=1)=0.5·0.15 + 0.3·0.7 + 0.2·0.25 = 0.335 P(Y=2)=0.5·0.05 + 0.3·0.2 + 0.2·0.7 = 0.225 H(Y)=[0.44·log(0.44) + 0.335·log(0.335) + 0.225·log(0.225)] H 1.5334 P(X,Y): P(0,0)=0.4 ; P(0,1)=0.075 ; P(0,2)=0.025 P(1,0)=0.03 ; P(1,1)=0.21 ; P(1,2)=0.06 P(2,0)=0.01 ; P(2,1)=0.05 ; P(2,2)=0.14 H(X,Y)=[P·log(P)] H 2.4898 H(Y|X): H(Y|X=0)=0.8842 ; H(Y|X=1)=1.1568 ; H(Y|X=2)=1.1219 H(Y|X)=0.5·0.8842 + 0.3·1.1568 + 0.2·1.1219 H 1.0135 I(X;Y)=H(Y)H(Y|X)=1.53341.0135=0.5198 Efic=I/H(X)=0.5198/1.4855=35% Capacidad rel=I/log(3)=0.5198/1.585=32.8% =á EJ2: CANAL AWGN B=1e6 ; N=1e-9 ; Pmax=1e-3 ; R=1.5e6 Pn = N·B = 1e-3 SNR = Pmax/Pn = 1 Capacidad: C = B·log(1+SNR) = 1e6·log(2) = 1e6 bps = 1 Mbps R > C No es posible sin errores Opciones: 1) B: Bnuevo = R/log(1+SNR) = 1.5 MHz 2) P: SNRreq=2^1.51=2.828 Ò Preq = 2.828·Pn = 2.828 mW 3) R: Rmáx = C = 1 Mbps Prob error: Eb/N = SNR·B/R = 1e6/1.5e6 = 0.667 Pe = Q((2·0.667)) H Q(1.155) H 0.124 =Ì RECOMENDACIÓN: Inviable con R=1.5 Mbps y B=1 MHz sin potencia o anchoB Made with nCreator - tiplanet.org
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