% Chapter 5: Example 5.02
%
L = 5; N = 20;
x = [ones(1,L), zeros(1,N-L)];
xn = x' * ones(1,3);
xn = (xn(:))';
n = -N:1:2*N-1;
subplot(1,1,1);subplot(2,1,2);
stem(n,xn); xlabel('n'); ylabel('xtilde(n)')
title('Three periods of xtilde(n)')
axis([-N,2*N-1,-0.5,1.5])
%print -deps2 fg0502.eps
%
subplot(1,1,1)
% Part (b)1
L = 5; N = 20;
xn = [ones(1,L), zeros(1,N-L)];
Xk = dfs(xn,N);
magXk = abs([Xk(N/2+1:N) Xk(1:N/2+1)]);
k = [-N/2:N/2];
subplot(2,2,1); stem(k,magXk); axis([-N/2,N/2,-0.5,5.5])
xlabel('k'); ylabel('Xtilde(k)')
title('DFS of SQ. wave: L=5, N=20')
% Part (b)2
L = 5; N = 40;
xn = [ones(1,L), zeros(1,N-L)];
Xk = dfs(xn,N);
magXk = abs([Xk(N/2+1:N) Xk(1:N/2+1)]);
k = [-N/2:N/2];
subplot(2,2,2); stem(k,magXk); axis([-N/2,N/2,-0.5,5.5])
xlabel('k'); ylabel('Xtilde(k)')
title('DFS of SQ. wave: L=5, N=40')
% Part (b)3
L = 5; N = 60;
xn = [ones(1,L), zeros(1,N-L)];
Xk = dfs(xn,N);
magXk = abs([Xk(N/2+1:N) Xk(1:N/2+1)]);
k = [-N/2:N/2];
subplot(2,2,3); stem(k,magXk); axis([-N/2,N/2,-0.5,5.5])
xlabel('k'); ylabel('Xtilde(k)')
title('DFS of SQ. wave: L=5, N=60')
% Part (b)4
L = 7; N = 60;
xn = [ones(1,L), zeros(1,N-L)];
Xk = dfs(xn,N);
magXk = abs([Xk(N/2+1:N) Xk(1:N/2+1)]);
k = [-N/2:N/2];
subplot(2,2,4); stem(k,magXk); axis([-N/2,N/2,-0.5,7.5])
xlabel('k'); ylabel('Xtilde(k)')
title('DFS of SQ. wave: L=7, N=60')
%print -deps2 fg0502b.eps