L=5;
N=20;
xn=[ones(1,L),zeros(1,N-L)];
we=exp(-j*2*pi/N);
n=[0:1:N-1];
k=[0:1:N-1];
wn=n'*k;
xk=xn*(we.^wn);
Axk=abs(xk);
figure(1)
subplot(2,1,1);
stem(n,xn);
axis([0,N-1,0,1]);
xlabel('n');
ylabel('x(n)');
title('the Original Signal');
subplot(2,1,2);
stem(k,Axk);
axis([0,N-1,0,L]);
grid;
xlabel('k');
ylabel('X(k)');
title('the DFS of Original Signal');