% aifig1 -- Average-Interpolating Refinement of a sequence of averages.
%
% The figure shows (as a step function) the block averages 
% of the function sin(t), and (as dashed and dotted curves)
% several average-interpolating refinements to a resolution
% 5 scales finer.
%
% At the resolution of the plotting device, all of the refinements 
% are equal to the true underlying function, and are much closer to 
% that function than the piecewise constant function. 
%
global Fil2 Fil4 Fil6 Fil8
global EdgeFil2 EdgeFil4 EdgeFil6 EdgeFil8
%
t = (0:63) ./16 - 2;
ave = 16  .*(cos(t) - cos(t +1/16.));
Blocks = ave;
MaxOrd=8;
dt = t(2)-t(1);
vb = [ Blocks ; Blocks ]; vb = vb(:);
tb = [t ; (t+dt) ]; tb = tb(:);
%clf;
hold on
subplot(1,1,1)
plot(tb,vb)
title('1. Interpolating Averages of sin(t)')
%axis([0 1 0 1]); 
xlabel('t')
%
a = Blocks;
for j=1:5, 
  a = AIRefine(a,2,Fil2,EdgeFil2); 
end;
t = 4 * (0:(length(a)-1)) ./ length(a) - 2;
plot(t,a,'--')
%
a = Blocks;
for j=1:5, 
  a = AIRefine(a,4,Fil4,EdgeFil4); 
end;
plot(t,a,'-.')
%
if(MaxOrd > 6),
a = Blocks;
for j=1:5, 
  a = AIRefine(a,8,Fil8,EdgeFil8); 
end;
plot(t,a,':')
end;
UnlockAxes






    
    
 
 
%
%  Part of Wavelab Version 850
%  Built Tue Jan  3 13:20:41 EST 2006
%  This is Copyrighted Material
%  For Copying permissions see COPYING.m
%  Comments? e-mail wavelab@stat.stanford.edu 
