To write a MATLAB script to represent a continuous time periodic signal in trigonometric Fourier series

Fourier series representation of ramp Input

clear all;

close all;

clc;

T=input('Enter the time period');

syms t

pi=3.14;

w=(2*pi)/T; sum=0;

x=t; %input signal

ao=(1/T)*int(x,t,-T/2,T/2);

%finding the coefficients

for n=1:11

an=(2/T)*int(x*cos(n*w*t),t,-T/2,T/2);

bn=(2/T)*int(x*sin(n*w*t),t,-T/2,T/2);

sum=sum+(an*cos(n*w*t)+bn*sin(n*w*t));

end

fplot(t,x,[-T/2,T/2]);

grid on; hold on;

fplot(t,(sum+ao),[-T/2,T/2]);

xlabel('t');

ylabel('Amplitude');

title('input signal and its Fourier Series representation');

legend('input', 'Fourier series')

 

Fourier series representation of exponential Input

clear all;

close all;

clc;

T=input('Enter the time period');

syms t

pi=3.14;

w=(2*pi)/T;

sum=0;

x=exp(t); %input signal

ao=(1/T)*int(x,t,-T/2,T/2);

%finding the coefficients

for n=1:11

an=(2/T)*int(x*cos(n*w*t),t,-T/2,T/2);

bn=(2/T)*int(x*sin(n*w*t),t,-T/2,T/2);

sum=sum+(an*cos(n*w*t)+bn*sin(n*w*t));

end

fplot(t,x,[-T/2,T/2]);

grid on;

hold on;

fplot(t,(sum+ao),[-T/2,T/2]);

xlabel('t');

ylabel('Amplitude');

title('input signal and its Fourier Series representation');

legend('input','Fourier series')