%% ----------------------------------------------------------
%%             START   N=5
%% ----------------------------------------------------------
N = 5; k = 0:1:N-1;                             % sample index
wk = 2*pi*k/N; zk = exp(j*wk);                  % samples of z
Xk = (zk)./(zk-0.7);                            % DFS as samples of X(z)
xn = real(idfs(Xk,N));                          % IDFS
xtilde = xn‘*ones(1,8); xtilde = (xtilde(:))‘;  % Periodic sequence

figure(‘NumberTitle‘, ‘off‘, ‘Name‘, ‘Example5.5‘)
set(gcf,‘Color‘,‘white‘); 
subplot(2,2,1); stem(0:39, xtilde); axis([0, 40, -0.1, 1.5]);
xlabel(‘n‘); ylabel(‘xtilde(n)‘); grid on;
title(‘N=5‘);
%% -----------------------------------------------------------
%%             END    N=5
%% -----------------------------------------------------------


%% ----------------------------------------------------------
%%             START   N=10
%% ----------------------------------------------------------
N = 10; k = 0:1:N-1;                            % sample index
wk = 2*pi*k/N; zk = exp(j*wk);                  % samples of z
Xk = (zk)./(zk-0.7);                            % DFS as samples of X(z)
xn = real(idfs(Xk,N));                          % IDFS
xtilde = xn‘*ones(1,4); xtilde = (xtilde(:))‘;  % Periodic sequence

subplot(2,2,2); stem(0:39, xtilde); axis([0, 40, -0.1, 1.5]);
xlabel(‘n‘); ylabel(‘xtilde(n)‘); grid on;
title(‘N=10‘);
%% ----------------------------------------------------------
%%             END   N=10
%% ----------------------------------------------------------


%% ----------------------------------------------------------
%%             START   N=20
%% ----------------------------------------------------------
N = 20; k = 0:1:N-1;                            % sample index
wk = 2*pi*k/N; zk = exp(j*wk);                  % samples of z
Xk = (zk)./(zk-0.7);                            % DFS as samples of X(z)
xn = real(idfs(Xk,N));                          % IDFS
xtilde = xn‘*ones(1,2); xtilde = (xtilde(:))‘;  % Periodic sequence

subplot(2,2,3); stem(0:39, xtilde); axis([0, 40, -0.1, 1.5]);
xlabel(‘n‘); ylabel(‘xtilde(n)‘); grid on;
title(‘N=20‘);
%% ----------------------------------------------------------
%%             END   N=20
%% ----------------------------------------------------------


%% ----------------------------------------------------------
%%             START   N=40
%% ----------------------------------------------------------
N = 40; k = 0:1:N-1;                            % sample index
wk = 2*pi*k/N; zk = exp(j*wk);                  % samples of z
Xk = (zk)./(zk-0.7);                            % DFS as samples of X(z)
xn = real(idfs(Xk,N));                          % IDFS
xtilde = xn‘*ones(1,1); xtilde = (xtilde(:))‘;  % Periodic sequence

subplot(2,2,4); stem(0:39, xtilde); axis([0, 40, -0.1, 1.5]);
xlabel(‘n‘); ylabel(‘xtilde(n)‘); grid on;
title(‘N=40‘);
%% ----------------------------------------------------------
%%             END   N=40
%% ----------------------------------------------------------