Fourier

LABORATORIO ANALISIS DE SEÑALES
SERIES DE FOURIER

Grafica asignada:

7.

Sea la serie de Fourier:

ft=a02+k=1∞[an*cosnπtL+bn*sennπtL]

Se evalúa la sumatoria en k=1, 6, 20,100SOLUCION:

t=linspace(-3,3,4000);
x=(t+2).*(-2<=t&t<-1)+(0).*(-1<=t & t<0)+(-t).*(0<=t & t<1)+(-1).*(1<=t & t<2);
xx=plot(t,x);set (xx,'LineWidth',1);
grid on
title ({'Series de Fourier'},'Color','k','fontsize',10,'fontweight','b')xlabel('Tiempo','Color','k','fontsize',10,'fontweight','b')
ylabel('Amplitud','Color','k','fontsize',10,'fontweight','b')
xlim([-2 4])
ylim([-2 2])
hold on

syms t1k
a0=(1/4)*(int(t1+2,-2,-1)+int(-t1,0,1)+int(-1,t1,1,2));
disp(a0)ak=(1/4)*(int((t1+2)*cos((pi*k*t1)/4),t1,-2,-1)+int((-t1)*cos((pi*k*t1)/4),t1,0,1)+int(-1*cos((pi*k*t1)/4),t1,1,2));
disp(ak)
bk=(1/4)*(int((t1+2)*sin((pi*k*t1)/4),t1,-2,-1)+int((-t1)*sin((pi*k*t1)/4),t1,0,1)+int(-1*sin((pi*k*t1)/4),t1,1,2));
disp(bk)suma=0;
for k=1:a %Valores de k 1,6,20,100
AK=eval(ak);
BK=eval(bk);s1=(AK.*cos((pi*k.*t)/4)+BK.*sin((pi*k.*t)/4));
suma=suma+s1;
end
s=(a0/2)+suma;
xxl=plot(t,s);
set(xxl,'LineWidth',1,'color','r');

a0 = -1/4

ak =(32*sin((pi*k)/8)^2 - 4*pi*k*sin((pi*k)/4))/(4*pi^2*k^2) - (8*sin((pi*k)/8)^2 - 8*sin((pi*k)/4)^2 + pi*k*sin((pi*k)/4))/(pi^2*k^2) - (sin((pi*k)/2) - sin((pi*k)/4))/(pi*k)

bk = (cos((pi*k)/2) -cos((pi*k)/4))/(pi*k) - (16*sin((pi*k)/4) - 32*cos((pi*k)/4)*sin((pi*k)/4) + 4*pi*k*cos((pi*k)/4))/(4*pi^2*k^2) - (16*sin((pi*k)/4) - 4*pi*k*cos((pi*k)/4))/(4*pi^2*k^2)

Con k=1

Con k=6

Con k=20

Con k =...