%The phase and energy distribution of white noise plus some common signal

clear;
figure(1); clf; hold on; 

N=60;

for ct=2,

  x=randn(N,1);
  y=randn(N,1);
  col='r';
  if ct==2,
    y=x+y;
  end;

fx=fftshift(fft(x)); 
fy=fftshift(fft(y)); 
fx=fx(1:end/2); 
fy=fy(1:end/2); 
ds=1/N; 
s=[0:ds:ds*(N/2-1)]'; 
axis tight;

Pxy=abs(fx.*conj(fy)); 
phi=angle(fx.*conj(fy)); 

subplot(311); hold on;
plot(x,'k'); 
plot(y,'r'); 
h=ylabel('realization');  font(h,16); 
h=xlabel('time');  font(h,16); 
font(gca,16); 
axis tight;

subplot(3,1,[2 3]); hold on;
for ct=1:N/2,
  polar([phi(ct) phi(ct)],[0 Pxy(ct)],[col,'.-']); 
end;
h=ylabel('imaginary part of \Phi_{xy}');  font(h,16); 
h=xlabel('real part of \Phi_{xy}');  font(h,16); 
font(gca,16); 
grid on;
axis equal; 
%axis tight; 


end;