Question

with matlab please

kx Gner a aiodic Sind xct) with f, frequerey 2π.thet is 2j2n -+- ae 2イ -r i ”イ .S

Answer 1

you had already derived all the coefficients:

and got the x(t)=x=1+ {(2/3)*cos(6*pi*t)}+ {cos(4*pi*t)} + {(1/2)*cos(2*pi*t)}

I devided the x(t) into three parts like X₁, X₂, X₃

_{first i plot individual plots like X1=}(2/3)*cos(6*pi*t)

X2=cos(4*pi*t)

X3=(1/2)*cos(2*pi*t)

Matlab code for X(t):

clc;clear all;close all;
t=-3:0.01:3;

x1=(2/3)*cos(6*pi*t);
subplot(2,2,1)
plot(t,x1)
grid on
title('Plotting x1=(2/3)*cos(6*pi*t)')

x2=cos(4*pi*t);
subplot(2,2,2)
plot(t,x2)
grid on
title('Plotting x2=cos(4*pi*t)')

x3=(1/2)*cos(2*pi*t);
subplot(2,2,3)
plot(t,x3)
grid on
title('Plotting x3=(1/2)*cos(2*pi*t)')

x=1+(2/3)*cos(6*pi*t)+cos(4*pi*t)+(1/2)*cos(2*pi*t);
subplot(2,2,4)
plot(t,x)
grid on
title('plotting x(t)')

plots:

final plot:

Plotting x1 (2/3)cos (6 pit) Plotting x2-cos(4 pi*t) 0.5 0.5 0.5 -3 .2 Plotting x3 (1/2) cos(2 pi't) plotting x(t) 0.5 0.5

3.5 1.5 0.5 0.5

if any doubts please comment me.