%demonstrating coherence between different records using the multi-taper method
%
%Two time-series are generated and you are asked to guesse whether they are 
%coherent or incoherent.  Coherent and incoherent time-series are generated
%at random.  
%
%Methods 2 through 4 are incoherent, while 1 and 5 produce coherent time-series.

figure(1); clf; hold on;
N=100;

for ct=1:100;

  choose=round(rand*5+0.5);
  
if choose==2 | choose==3,
  x=detrend(normPH(cumsum(randn(N,1))));
  y=detrend(normPH(cumsum(randn(N,1)))); 
end;
if choose==4,
  x=normPH(conv([1 -1 1 1],randn(N,1)));
  y=normPH(conv([1 -1 1 1],randn(N,1)));
end;
if choose==1,
  x=randn(N,1); 
  y=conv([-1 -3 -3 2 1 0.5],x);
  y=y(3:end-3); 
end;
if choose==5,
  x=randn(N,1); 
  y=conv([-1 -3 -3 2 1 0.5],x);
  y=y(3:end-3); 
  x=cumsum(x); 
end;

figure(1); clf; hold on;
plot(x,'k'); 
plot(y,'r'); 
axis tight; 
h=ylabel('realization'); font(h,16); 
h=xlabel('time'); font(h,16); 
font(gca,16);

pause;

figure(2); clf; hold on;
nw=4;
cmtm(x,y,1,nw,0,0,1); 
subplot(211); 
if (choose==1 | choose==5),
  h=text(1/80,0.85,'Coherent'); font(h,42); 
else;
  h=text(1/80,0.85,'Incoherent'); font(h,42); 
end;

pause;
end;