%The phase and energy distribution of white noise

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

N=50;

for ct=1; %:2,
if ct==1,
  x=randn(N,1);
  col='r';
else;
  x=cumsum(x);
  col='k'
end;

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

P=f.*conj(f); 
phi=angle(f); 

subplot(311); hold on;
plot(x,col); 
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 P(ct)],[col,'.-']); 
end;
h=ylabel('b_k ');  font(h,16); 
h=xlabel('a_k ');  font(h,16); 
font(gca,16); 
grid on;
axis equal; 
%axis tight; 


end;