%Fourier series of  rectangular wave
clc;
close all;
clear all;

j=1;
T=4;    %Time period of square wave
tau=1;  %2tau= On time of the square wave
w0=2*pi/T;
N=50; 
j=1;
for k=-N:1:N 
    if(k==0)
        c(j)=2*tau/T;   % fourier series coefficients of rectangular pulse
    else
        c(j)=2*sin(k*w0*tau)/(k*w0*T);
    end
   j=j+1;
end
k=-N:1:N;
subplot(2,1,1);
stem(k,c);      %plot fourier series coefficients
grid on;
xlabel('k');
ylabel('fourier series coefficient of rectangular pulse');

%%----------------------------------------------------
l=1;
time=10;
for t=-time:0.01:time
    sum=0;
    j=1;
    for k=-N:1:N
        sum=sum+c(j)*exp(i*k*w0*t); %synthesis equation
        j=j+1;
    end
    s(l)=sum;
    l=l+1;
end
t=-time:0.01:time
subplot(2,1,2);
plot(t,s);          % plot rectangular pulse
grid on;
xlabel('time');
ylabel('rectangular pulse');