% fg_03_11 Linear phase shift.
Ns=20; Nz=30; K=4;
N=Ns+Nz;
s=sin(pi*[0:Ns-1]/Ns);
x=[s,zeros(1,Nz)];
y=[zeros(1,K),s,zeros(1,Nz-K)];
X=fft(x);
Y=fft(y);
sp_fig(1);
% Plot x.
subplot(2,2,1);
axis([0 N -.4 1.4]);
set(gca,'fontsize',16)
line(0:N-1,x,'color','r','marker','o'); grid;
xlabel('Sample (n)'); ylabel('        x_n');
% Plot phase of x.
subplot(2,2,2);
phase=unwrap(angle(X(1:N/2+1)));
axis([0 N/2 -20 0]);
set(gca,'fontsize',16)
line(0:N/2,phase,'color','r','marker','o'); grid;
xlabel('Index (m)'); ylabel('X phase (rad)');
% Plot y.
subplot(2,2,3);
axis([0 N -.4 1.4]);
set(gca,'fontsize',16)
line(0:N-1,y,'color','b','marker','o'); grid;
xlabel('Sample (n)');
ylabel('  y_n = x_{n-k}');
% Plot phase of y.
subplot(2,2,4);
phase=unwrap(angle(Y(1:N/2+1)));
axis([0 N/2 -20 0]);
set(gca,'fontsize',16)
line(0:N/2,phase,'color','b','marker','o'); grid;
xlabel('Index (m)'); ylabel('Y phase (rad)');
text(16,-3,'-2\pimk/N','fontsize',16);
% Add line with slope -.50.
line(0:N/2,-.5*[0:N/2],'color','b','linestyle','--');