Contents

Ejercicio 2

%Hallar el vector X para la siguiente ecuación matricial 
 
 
 A=[4 -2 -10;2 10 -12;-4 -6 16]; 
 b=[-10 32 -16]'; 
 X=A\b 
 
 
 X = 
 
 
 2.0000 
 4.0000 
 1.0000

Ejercicio 4

%Hallar los autovalores y autovectores de la matriz A: 
 
 
 A=[0 1 -1;-6 -11 6;-6 -11 5]; 
 [X,D]=eig(A) 
 T1=A*X 
 T2=X*D 
 
 
 X = 
 
 
 0.7071 -0.2182 -0.0921 
 0.0000 -0.4364 -0.5523 
 0.7071 -0.8729 -0.8285 
 
 
 
 
 D = 
 
 
 -1.0000 0 0 
 0 -2.0000 0 
 0 0 -3.0000 
 
 
 
 
 T1 = 
 
 
 -0.7071 0.4364 0.2762 
 -0.0000 0.8729 1.6570 
 -0.7071 1.7457 2.4856 
 
 
 
 
 T2 = 
 
 
 -0.7071 0.4364 0.2762 
 -0.0000 0.8729 1.6570 
 -0.7071 1.7457 2.4856

Ejercicio 5

%Para el siguiente circuito, determinar los voltajes de los nodos V1 y V2 y la potencia 
 %entregada por cada fuente: 
 
 
 Y=[1.5-2.0i -0.35+1.2i;-0.35+1.2i 0.9-1.6i]; 
 I=[30+40i; 20+15i]; 
 disp('Solución:') 
 U=Y\I 
 S=U.*conj(I) 
 
Solución: 
 
 
 U = 
 
 
 3.5902 +35.0928i 
 6.0155 +36.2212i 
 
 
 
 
 S = 
 
 
 1.0e+003 * 
 
 
 1.5114 + 0.9092i 
 0.6636 + 0.6342i

Ejercicio 6

%Escribir una función recursiva para resolver el problema de la Torres de Hanoi y 
 %probarla para un valor 5 discos. 
 
 
 % Torres de Hanoi 
 % uso: hanoi(N,Tini,Taux,Tdes) 
 % donde N=numero de discos (entero>0) 
 % Tini = torre inicial (caracter i.e. 'a') 
 % Taux = torre auxiliar (caracter i.e. 'b') 
 % Tdes = torre destino (caracter i.e. 'c') 
 
 
 
 
 % function hanoi(n,i,a,f) 
 % if n>0 
 % hanoi(n-1,i,f,a); 
 % fprintf('mover disco %d de %c a %c\n',n,i,f); 
 % hanoi(n-1,a,i,f); 
 % end 
 % end 
 
 
 hanoi(5,'a','b','c') 
 
mover disco 1 de a a c 
 mover disco 2 de a a b 
 mover disco 1 de c a b 
 mover disco 3 de a a c 
 mover disco 1 de b a a 
 mover disco 2 de b a c 
 mover disco 1 de a a c 
 mover disco 4 de a a b 
 mover disco 1 de c a b 
 mover disco 2 de c a a 
 mover disco 1 de b a a 
 mover disco 3 de c a b 
 mover disco 1 de a a c 
 mover disco 2 de a a b 
 mover disco 1 de c a b 
 mover disco 5 de a a c 
 mover disco 1 de b a a 
 mover disco 2 de b a c 
 mover disco 1 de a a c 
 mover disco 3 de b a a 
 mover disco 1 de c a b 
 mover disco 2 de c a a 
 mover disco 1 de b a a 
 mover disco 4 de b a c 
 mover disco 1 de a a c 
 mover disco 2 de a a b 
 mover disco 1 de c a b 
 mover disco 3 de a a c 
 mover disco 1 de b a a 
 mover disco 2 de b a c 
 mover disco 1 de a a c

Ejercicio 7

%Ajustar un polinomio de orden 2 a los siguientes datos: 
 
 
 x=0:0.5:5; 
 y=[10 10 16 24 30 38 52 68 82 96 123]; 
 p=polyfit(x,y,2) 
 yc=polyval(p,x); 
 plot(x,y,'x',x,yc); 
 xlabel('x'),ylabel('y'),grid,title('Ajuste polinómico') 
 legend('Datos','Ajuste polinómico',4) 
 
 
 p = 
 
 
 4.0233 2.0107 9.6783

Ejercicio 8

%Partir la ventana Figure en cuatro particiones (2x2) y graficar las siguientes funciones 
 %para wt de 0 a 3p en pasos de 0.05 
 
 
 wt=0:0.05:3*pi; 
 v=120*sin(wt); 
 i=100*sin(wt-pi/4); 
 p=v.*i; 
 subplot(2,2,1) 
 plot(wt,v,wt,i) 
 title('Voltaje y Corriente'),xlabel('\omegat,radianes') 
 subplot(2,2,2) 
 plot(wt,p) 
 title('Potencia'),xlabel('\omegat, radianes') 
 Fm=3.0; 
 fa=Fm*sin(wt); 
 fb=Fm*sin(wt-2*pi/3); 
 fc=Fm*sin(wt-4*pi/3); 
 subplot(2,2,3) 
 plot(wt,fa,wt,fb,wt,fc) 
 title('Fm trifásico'),xlabel('\omegat,radianes') 
 fR=3/2*Fm; 
 subplot(2,2,4) 
 plot(-fR*cos(wt),fR*sin(wt)) 
 title('Fm rotante')

Ejercicio 11

p=[1 0 -35 50 24]; 
 sol=roots(p) 
 
 
 sol = 
 
 
 -6.4910 
 4.8706 
 2.0000 
 -0.3796

Ejercicio 12

% function Ejemploode 
 % [t,yy]=ode45(@HalfSine,[0 35],[1 0],[], 0.15) 
 % plot(t,yy(:,1)) 
 % function y= HalfSine(t,y,z) 
 % h=sin(pi*t/5).*(t<=5); 
 % y=[y(2); -2*z*y(2)-y(1)+h]; 
 % <html> 
 % <ul> 
 % <li>y(0) 
 % 
 % </ul> 
 % </html> 
 
 
 Ejemploode 
 
 
 t = 
 
 
 0 
 0.0001 
 0.0001 
 0.0002 
 0.0002 
 0.0005 
 0.0007 
 0.0010 
 0.0012 
 0.0025 
 0.0037 
 0.0050 
 0.0062 
 0.0125 
 0.0188 
 0.0251 
 0.0313 
 0.0627 
 0.0941 
 0.1255 
 0.1569 
 0.3139 
 0.4709 
 0.6279 
 0.7849 
 0.9876 
 1.1902 
 1.3929 
 1.5955 
 1.7883 
 1.9810 
 2.1737 
 2.3664 
 2.5405 
 2.7147 
 2.8889 
 3.0631 
 3.2630 
 3.4630 
 3.6630 
 3.8630 
 4.0787 
 4.2944 
 4.5102 
 4.7259 
 4.9135 
 5.1012 
 5.2888 
 5.4764 
 5.7052 
 5.9339 
 6.1626 
 6.3913 
 6.5871 
 6.7829 
 6.9787 
 7.1745 
 7.3714 
 7.5683 
 7.7652 
 7.9620 
 8.1430 
 8.3240 
 8.5050 
 8.6860 
 8.8903 
 9.0946 
 9.2989 
 9.5032 
 9.6971 
 9.8910 
 10.0850 
 10.2789 
 10.4720 
 10.6650 
 10.8581 
 11.0511 
 11.2365 
 11.4219 
 11.6072 
 11.7926 
 11.9916 
 12.1907 
 12.3897 
 12.5887 
 12.7863 
 12.9839 
 13.1815 
 13.3790 
 13.5672 
 13.7553 
 13.9435 
 14.1316 
 14.3213 
 14.5110 
 14.7007 
 14.8904 
 15.0840 
 15.2775 
 15.4711 
 15.6646 
 15.8662 
 16.0678 
 16.2693 
 16.4709 
 16.6537 
 16.8364 
 17.0191 
 17.2019 
 17.3961 
 17.5903 
 17.7844 
 17.9786 
 18.1664 
 18.3541 
 18.5418 
 18.7295 
 18.9355 
 19.1415 
 19.3474 
 19.5534 
 19.7300 
 19.9066 
 20.0832 
 20.2598 
 20.4587 
 20.6576 
 20.8566 
 21.0555 
 21.2367 
 21.4179 
 21.5992 
 21.7804 
 21.9913 
 22.2023 
 22.4132 
 22.6241 
 22.7941 
 22.9640 
 23.1339 
 23.3039 
 23.5079 
 23.7120 
 23.9160 
 24.1201 
 24.2937 
 24.4673 
 24.6410 
 24.8146 
 25.0313 
 25.2479 
 25.4646 
 25.6812 
 25.8613 
 26.0413 
 26.2213 
 26.4014 
 26.6116 
 26.8218 
 27.0320 
 27.2422 
 27.4117 
 27.5812 
 27.7506 
 27.9201 
 28.1397 
 28.3592 
 28.5787 
 28.7983 
 28.9828 
 29.1672 
 29.3517 
 29.5362 
 29.7425 
 29.9487 
 30.1550 
 30.3613 
 30.5340 
 30.7068 
 30.8795 
 31.0523 
 31.2672 
 31.4822 
 31.6972 
 31.9122 
 32.0993 
 32.2864 
 32.4736 
 32.6607 
 32.8631 
 33.0656 
 33.2680 
 33.4704 
 33.6470 
 33.8235 
 34.0001 
 34.1767 
 34.3825 
 34.5883 
 34.7942 
 35.0000 
 
 
 
 
 yy = 
 
 
 1.0000 0 
 1.0000 -0.0001 
 1.0000 -0.0001 
 1.0000 -0.0002 
 1.0000 -0.0002 
 1.0000 -0.0005 
 1.0000 -0.0007 
 1.0000 -0.0010 
 1.0000 -0.0012 
 1.0000 -0.0025 
 1.0000 -0.0037 
 1.0000 -0.0050 
 1.0000 -0.0062 
 0.9999 -0.0124 
 0.9998 -0.0186 
 0.9997 -0.0248 
 0.9995 -0.0309 
 0.9981 -0.0609 
 0.9957 -0.0899 
 0.9924 -0.1180 
 0.9883 -0.1451 
 0.9557 -0.2651 
 0.9064 -0.3584 
 0.8447 -0.4243 
 0.7747 -0.4631 
 0.6788 -0.4747 
 0.5847 -0.4465 
 0.5002 -0.3839 
 0.4312 -0.2937 
 0.3844 -0.1896 
 0.3587 -0.0748 
 0.3558 0.0434 
 0.3754 0.1580 
 0.4113 0.2530 
 0.4628 0.3352 
 0.5271 0.4008 
 0.6012 0.4468 
 0.6938 0.4724 
 0.7883 0.4671 
 0.8784 0.4301 
 0.9581 0.3624 
 1.0258 0.2576 
 1.0675 0.1243 
 1.0777 -0.0317 
 1.0524 -0.2033 
 0.9994 -0.3619 
 0.9171 -0.5141 
 0.8081 -0.6438 
 0.6773 -0.7438 
 0.4969 -0.8246 
 0.3035 -0.8584 
 0.1078 -0.8465 
 -0.0803 -0.7928 
 -0.2287 -0.7177 
 -0.3601 -0.6204 
 -0.4705 -0.5056 
 -0.5571 -0.3785 
 -0.6185 -0.2439 
 -0.6532 -0.1078 
 -0.6613 0.0243 
 -0.6440 0.1480 
 -0.6078 0.2508 
 -0.5541 0.3401 
 -0.4856 0.4138 
 -0.4054 0.4704 
 -0.3044 0.5129 
 -0.1973 0.5321 
 -0.0886 0.5286 
 0.0172 0.5040 
 0.1113 0.4632 
 0.1960 0.4078 
 0.2687 0.3408 
 0.3275 0.2650 
 0.3710 0.1843 
 0.3986 0.1014 
 0.4102 0.0197 
 0.4064 -0.0582 
 0.3891 -0.1270 
 0.3598 -0.1878 
 0.3201 -0.2390 
 0.2718 -0.2795 
 0.2129 -0.3102 
 0.1492 -0.3272 
 0.0836 -0.3307 
 0.0185 -0.3212 
 -0.0431 -0.3003 
 -0.0996 -0.2691 
 -0.1489 -0.2297 
 -0.1898 -0.1838 
 -0.2200 -0.1360 
 -0.2409 -0.0862 
 -0.2524 -0.0362 
 -0.2546 0.0123 
 -0.2479 0.0581 
 -0.2329 0.0993 
 -0.2106 0.1348 
 -0.1822 0.1635 
 -0.1482 0.1854 
 -0.1109 0.1994 
 -0.0716 0.2052 
 -0.0319 0.2033 
 0.0082 0.1936 
 0.0457 0.1769 
 0.0791 0.1542 
 0.1075 0.1268 
 0.1282 0.0990 
 0.1436 0.0694 
 0.1535 0.0392 
 0.1579 0.0094 
 0.1568 -0.0210 
 0.1500 -0.0488 
 0.1381 -0.0732 
 0.1218 -0.0936 
 0.1027 -0.1090 
 0.0811 -0.1199 
 0.0580 -0.1260 
 0.0341 -0.1275 
 0.0081 -0.1240 
 -0.0167 -0.1157 
 -0.0392 -0.1031 
 -0.0589 -0.0870 
 -0.0729 -0.0712 
 -0.0839 -0.0539 
 -0.0919 -0.0360 
 -0.0966 -0.0179 
 -0.0982 0.0020 
 -0.0959 0.0207 
 -0.0901 0.0375 
 -0.0811 0.0519 
 -0.0707 0.0626 
 -0.0586 0.0707 
 -0.0453 0.0761 
 -0.0312 0.0788 
 -0.0145 0.0786 
 0.0018 0.0751 
 0.0170 0.0685 
 0.0305 0.0594 
 0.0398 0.0506 
 0.0476 0.0408 
 0.0537 0.0304 
 0.0579 0.0196 
 0.0606 0.0066 
 0.0607 -0.0058 
 0.0583 -0.0173 
 0.0537 -0.0273 
 0.0483 -0.0346 
 0.0418 -0.0405 
 0.0343 -0.0449 
 0.0263 -0.0477 
 0.0157 -0.0491 
 0.0052 -0.0482 
 -0.0050 -0.0452 
 -0.0143 -0.0403 
 -0.0211 -0.0350 
 -0.0268 -0.0290 
 -0.0315 -0.0223 
 -0.0349 -0.0153 
 -0.0372 -0.0070 
 -0.0378 0.0011 
 -0.0368 0.0087 
 -0.0342 0.0154 
 -0.0312 0.0200 
 -0.0275 0.0239 
 -0.0232 0.0269 
 -0.0184 0.0290 
 -0.0119 0.0304 
 -0.0052 0.0302 
 0.0013 0.0287 
 0.0073 0.0259 
 0.0118 0.0228 
 0.0157 0.0191 
 0.0188 0.0150 
 0.0212 0.0105 
 0.0229 0.0055 
 0.0235 0.0005 
 0.0231 -0.0042 
 0.0218 -0.0084 
 0.0200 -0.0115 
 0.0178 -0.0142 
 0.0152 -0.0162 
 0.0122 -0.0177 
 0.0083 -0.0187 
 0.0042 -0.0189 
 0.0003 -0.0182 
 -0.0035 -0.0167 
 -0.0065 -0.0148 
 -0.0090 -0.0126 
 -0.0112 -0.0101 
 -0.0128 -0.0073 
 -0.0140 -0.0043 
 -0.0145 -0.0012 
 -0.0145 0.0017 
 -0.0138 0.0044 
 -0.0129 0.0065 
 -0.0116 0.0083 
 -0.0100 0.0097 
 -0.0082 0.0107 
 -0.0059 0.0115 
 -0.0035 0.0117 
 -0.0011 0.0115 
 0.0012 0.0108

Ejercicio 13

Tomando como base las condiciones del ejemplo de la transformada de Fourier de los apuntes (pág. 124), graficar para las siguientes señales la gráfica de la señal en el tiempo y la gráfica de la amplitud espectral en función de la frecuencia:

k=5;m=10;fo=10;Bo=2.5;N=2^m;T=2^k/fo; 
 ts=(0:N-1)*T/N;df=(0:N/2-1)/T; 
 SampledSignal = Bo*sin(2*pi*fo*ts)+Bo/2*sin(2*pi*fo*2*ts); 
 An=abs(fft(SampledSignal, N))/N; 
 subplot(2,2,1) 
 plot(df,2*An(1:N/2)) 
 
 
 
 
 k=5;m=10;fo=10;N=2^m;T=2^k/fo; 
 ts=(0:N-1)*T/N;df=(0:N/2-1)/T; 
 SampledSignal=exp(-2*ts).*sin(2*pi*fo*ts); 
 An=abs(fft(SampledSignal,N))/N; 
 subplot(2,2,2) 
 plot(df,2*An(1:N/2)) 
 
 
 
 
 k=5;m=10;fo=10;N=2^m;T=2^k/fo; 
 ts=(0:N-1)*T/N;df=(0:N/2-1)/T; 
 SampledSignal=sin(2*pi*fo*ts+5*sin(2*pi*(fo/10)*ts)); 
 An=abs(fft(SampledSignal,N))/N; 
 subplot(2,2,3) 
 plot(df,2*An(1:N/2)) 
 
 
 
 
 k=5;m=10;fo=10;N=2^m;T=2^k/fo; 
 ts=(0:N-1)*T/N;df=(0:N/2-1)/T; 
 SampledSignal=sin(2*pi*fo*ts-5*exp(-2*ts)); 
 An=abs(fft(SampledSignal,N))/N; 
 subplot(2,2,4) 
 plot(df,2*An(1:N/2))

Ejercicio 14

Leer y graficar la imagen WindTunnel.jpg de las transparencias y graficar en sendos gráficos el valor del color rojo de la imagen en función del ancho de la imagen y el histograma del mismo para una fila de la imagen que se pide al usuario. Mostrar el valor para 200

A=imread('WindTunnel.jpg','jpeg'); 
 row=200; 
 red=A(row,:,1); 
 gr=A(row,:,2); 
 bl=A(row,:,3); 
 
 
 subplot(2,1,1) 
 plot(red,'r'); 
 title('Distribución del color rojo en la fila 200') 
 %hold on 
 %plot(gr,'g'); 
 %plot(bl,'b'); 
 subplot(2,1,2) 
 hist(red,0:15:255); 
 title('Histograma del color rojo en la fila 200'); 
 hold off