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function sy = synth2d(an,fopt,levs) 
%Routine to reconstruct the 2-D image from its orthonormal DWT. Circular 
%extension used to extend the subbands. 
% 
%This routine is complement to the analysis routine 'anal2d'. 
% 
%sy = synth2d(an,lpf,L) takes the L level DWT of the 2-D image  
%and reconstructs it using the orthonormal synthesis filter bank 
%defined by the filter lpf. The reconstructed image is stored in  
%the matrix 'sy'. If lpf corresponds to the analysis filter used  
%for the DWT, then perfect reconstruction will be obtained. 
% 
%sy = synth2d(an,fopt,L) takes the L level DWT of the 2-D image 
%and reconstructs it using the synthesis filter bank defined by a  
%filter stored in the routine. This is chosen using the variable fopt. 
%The reconstructed image is stored in the matrix 'sy'. If the  
%synthesis filter bank thus chosen corresponds to the analysis  
%filter bank used then perfect recontruction will be obtained. 
% 
%The input variables are: 
%an   : 2-D array containing the DWT. 
%lpf  : Lowpass filter used to construct the synthesis filter bank. 
%OR  
%fopt : which can take a value from 1 to 5 and corresponds to Daubechies 
%       2*fopt tap filters respectively 
%L    : The number of levels down to which the DWT has been performed. 
% 
%The reconstructed image stored in 'sy' can be displayed using the  
%image or the imagesc command along with the colormap command. Please 
%refer to MATLAB help for more information on these commands. 
% 
%The reconstructed image is displayed at the end of the routine. 
% 
%Refer to Chapter 4 for more information on 2-D separable DWT.  
% 
%Author: Ajit S. Bopardikar 
%Copyright (c) 1998 by Addison Wesley Longman, Inc. 
% 
 
  if(prod(size(fopt))==1) %you want to use one of the filter options... 
    if (fopt==1) %Daubechies 2 or Haar case 
       lpf = [1/sqrt(2) 1/sqrt(2)]; 
    elseif (fopt == 2) %Daubechies 4 
      lpf =[0.48296291314453 0.83651630373781 0.22414386804201 -0.12940952255126]; 
    elseif (fopt == 3) %Daubechies 6 
      lpf =[0.33267055295000 0.80689150931100 0.45877502118000 -0.13501102001000 -0.08544127388200 0.03522629188200]; 
    elseif (fopt == 4) %Daubechies 8 
      lpf =[0.23037781330900 0.71484657055300 0.63088076793000 -0.02798376941700 -0.18703481171900 0.03084138183600 0.03288301166700 -0.01059740178500]; 
    elseif (fopt >= 5) %Daubechies 10 
      if (fopt > 5) 
      fprintf('fopt chosen to be greater than 5. Using fopt=5 instead\n'); 
      end;  
      lpf =[0.16010239797400 0.60382926979700 0.72430852843800 0.13842814590100 -0.24229488706600 -0.03224486958500 0.07757149384000 -0.00624149021300 -0.01258075199900 0.00333572528500]; 
    end %end inner if 
  else %input filter 
    lpf = fopt; 
  end %end if 
  lf = length(lpf); 
  
  lo = lpf(lf:-1:1); 
 
   for i=0:(lf-1) 
     hpf(i+1) = (-1)^i*lpf(lf-i); 
   end; %end for 
   hi = hpf(lf:-1:1); 
%so we have the high pass filter here. 
 
   [m,n] = size(an); %dimensions of the original image 
 
   m = m/(2^levs); %the dimensions of  
   n = n/(2^levs); %lowest LL subband 
 
   an1 = an; 
 
   for i=1:levs 
     sy = synth21(an1(1:2*m,1:2*n),lo,hi); 
     an1(1:2*m,1:2*n) = sy; 
     m = 2*m; 
     n = 2*n; 
   end; %endfor 
   sy=sy+128; 
   %figure;colormap(gray);imagesc(sy);title('IDWT of input DWT array');  
   %imshow(mat2gray(sy));title('IDWT of input DWT array');