Frequency spectrum of a periodic signal

clc
clear all
close all
t=0:0.01:10;
x=[ones(1,201),zeros(1,99),ones(1,201),zeros(1,99),ones(1,201),zeros(1,99),ones(1,101)];
T=3;
w=2*pi/T;


dtau=0.1;
for k=-10:10
    sum = 0;
    i=1;
    for tau=0:dtau:T
        exp_part = exp(-j*w*k*tau)*dtau;
        sum = sum + exp_part.*x(i);
        i=i+1;
    end
    a(k+11) = sum;
end
for i=1:21
    mag(i) = abs(a(i));
    phase(i) = angle(a(i));
end
k=-10:10;
subplot(2,2,[1:2]);
plot(t,x);
title('Input Signal (A Pulse Train)');
xlabel('Time');
ylabel('Amlitudeof the signal');


subplot(2,2,3);
stem(k,mag);
title('Magnitude Spectra');
xlabel('k \rightarrow');
ylabel('Magnitude');


subplot(2,2,4);
stem(k,phase,'Linewidth',1.2);
title('Phase Spectra');
xlabel('k \rightarrow');
ylabel('Phase');