haarS = [1/sqrt(2),1/sqrt(2)];
haarW = [1/sqrt(2),-1/sqrt(2)];
N1=16;
X = FilterMatrix(haarS,N1);
Phi1 = X([1:2:N1],:);
X = FilterMatrix(haarW,N1);
Psi1 = X([1:2:N1],:);
W1N1 = [Phi1;Psi1]
W1N1'*W1N1

N2 = N1/2;
X = FilterMatrix(haarS,N2);
Phi2 = X([1:2:N2],:);
X = FilterMatrix(haarW,N2);
Psi2 = X([1:2:N2],:);
W1N2 = [Phi2;Psi2]
W1N2'*W1N2

% Make W2N1

W2N1 = [W1N2*Phi1;Psi1]
W2N1'*W2N1

% Now let's do the five levels with N1 = 1024
clear;
haarS = [1/sqrt(2),1/sqrt(2)];
haarW = [1/sqrt(2),-1/sqrt(2)];

Daub4S = [(1+sqrt(3))/sqrt(8),(3+sqrt(3))/sqrt(8),...
          (3-sqrt(3))/sqrt(8),(1-sqrt(3))/sqrt(8)];
Daub4W = [-(1-sqrt(3))/sqrt(8),(3-sqrt(3))/sqrt(8),...
          -(3+sqrt(3))/sqrt(8),(1+sqrt(3))/sqrt(8)];

S=Daub4S;
W=Daub4W;

N1=1024;
X1 = FilterMatrix(S,N1);
Phi1 = X1([1:2:N1],:);
X1 = FilterMatrix(W,N1);
Psi1 = X1([1:2:N1],:);

N2=N1/2;
X2 = FilterMatrix(S,N2);
Phi2 = X2([1:2:N2],:);
X2 = FilterMatrix(W,N2);
Psi2 = X2([1:2:N2],:);

N3=N2/2;
X3 = FilterMatrix(S,N3);
Phi3 = X3([1:2:N3],:);
X3 = FilterMatrix(W,N3);
Psi3 = X3([1:2:N3],:);

N4=N3/2;
X4 = FilterMatrix(S,N4);
Phi4 = X4([1:2:N4],:);
X4 = FilterMatrix(W,N4);
Psi4 = X4([1:2:N4],:);

N5=N4/2;
X5 = FilterMatrix(S,N5);
Phi5 = X5([1:2:N5],:);
X5 = FilterMatrix(W,N5);
Psi5 = X5([1:2:N5],:);

W5 = [ Phi5 * Phi4 * Phi3 * Phi2 * Phi1; ...
       Psi5 * Phi4 * Phi3 * Phi2 * Phi1; ...
       Psi4 * Phi3 * Phi2 * Phi1; ...
       Psi3 * Phi2 * Phi1; ...
       Psi2 * Phi1; ...
       Psi1];
   
 S = [cos(pi/128*[1:128]),cos(pi*2/128*[1:128]),...
      cos(4*pi/128*[1:128]),cos(pi*8/128*[1:128]),...
      cos(16*pi/128*[1:128]),cos(pi*32/128*[1:128]),...
      cos(64*pi/128*[1:128]),cos(pi*128/128*[1:128])]';
 WT = W5*S;
 
 Cells=zeros(6,512);
 Cells(1,[1:16:512]) = WT(1:32);
 Cells(1,[1:16:512]+1) = WT(1:32);
 Cells(1,[1:16:512]+2) = WT(1:32);
 Cells(1,[1:16:512]+3) = WT(1:32);
 Cells(1,[1:16:512]+4) = WT(1:32);
 Cells(1,[1:16:512]+5) = WT(1:32);
 Cells(1,[1:16:512]+6) = WT(1:32);
 Cells(1,[1:16:512]+7) = WT(1:32);
 Cells(1,[1:16:512]+8) = WT(1:32);
 Cells(1,[1:16:512]+9) = WT(1:32);
 Cells(1,[1:16:512]+10) = WT(1:32);
 Cells(1,[1:16:512]+11) = WT(1:32);
 Cells(1,[1:16:512]+12) = WT(1:32);
 Cells(1,[1:16:512]+13) = WT(1:32);
 Cells(1,[1:16:512]+14) = WT(1:32);
 Cells(1,[1:16:512]+15) = WT(1:32);
 
 Cells(2,[1:16:512]) = WT(33:64);
 Cells(2,[1:16:512]+1) = WT(33:64);
 Cells(2,[1:16:512]+2) = WT(33:64);
 Cells(2,[1:16:512]+3) = WT(33:64);
 Cells(2,[1:16:512]+4) = WT(33:64);
 Cells(2,[1:16:512]+5) = WT(33:64);
 Cells(2,[1:16:512]+6) = WT(33:64);
 Cells(2,[1:16:512]+7) = WT(33:64);
 Cells(2,[1:16:512]+8) = WT(33:64);
 Cells(2,[1:16:512]+9) = WT(33:64);
 Cells(2,[1:16:512]+10) = WT(33:64);
 Cells(2,[1:16:512]+11) = WT(33:64);
 Cells(2,[1:16:512]+12) = WT(33:64);
 Cells(2,[1:16:512]+13) = WT(33:64);
 Cells(2,[1:16:512]+14) = WT(33:64);
 Cells(2,[1:16:512]+15) = WT(33:64);
 
 Cells(3,[1:8:512]) = WT(65:128);
 Cells(3,[1:8:512]+1) = WT(65:128);
 Cells(3,[1:8:512]+2) = WT(65:128);
 Cells(3,[1:8:512]+3) = WT(65:128);
 Cells(3,[1:8:512]+4) = WT(65:128);
 Cells(3,[1:8:512]+5) = WT(65:128);
 Cells(3,[1:8:512]+6) = WT(65:128);
 Cells(3,[1:8:512]+7) = WT(65:128);
 
                      
 Cells(4,[1:4:512]) = WT(129:256);
 Cells(4,[1:4:512]+1) = WT(129:256);
 Cells(4,[1:4:512]+2) = WT(129:256);
 Cells(4,[1:4:512]+3) = WT(129:256);
 
 Cells(5,[1:2:512]) = WT(257:512);
 Cells(5,[1:2:512]+1) = WT(257:512);
 Cells(6,[1:1:512]) = WT(513:1024);