synthh.m

这是伯克里wavelet transforms一书中的例子的代码

function sy = synthh(anal,sl,sh,levs)
%Routine to reconstruct the  signal from its multilevel DWT using 
%an even length or half sample symmetric (HSS) biorthogonal filter bank. 
%Symmetric extension used to extend the subbands. This routine 
%complements the analysis routine 'analh'.
%
%sy = synthh(an,lpf,hpf,L) reconstructs the original signal from 
%its DWT, 'an', which could be the output of the analysis routine 'analh'.
%The signal is assumed to be decomposed to L levels. The HSS filter 
%bank used is comprised of lpf and hpf. If this corresponds to the 
%analysis filter bank used for decomposition then you get perfect 
%reconstruction.
%
%sy = synthh(an,fopt,L) reconstructs the original signal from 
%its DWT, 'an', which could be the output of the analysis routine 'analh'. 
%The signal is assumed to be decomposed to L levels. 
%fopt chooses a HSS synthesis filter bank provided in the routine. 
%If this corresponds to the analysis filter bank used for the 
%decomposition then you get perfect reconstruction.
%
%The final result of the synthesis procedure is plotted in the end.
%
%The input variables are
%an      : L-level DWT 
%lpf, hpf: these two filters define the synthesis filter bank
%OR
%fopt    :Takes the values of 1,2 or 3 and correspond to the 6/2 and 
%         2/6 and 4/4 tap filter banks respectively.
%L       : Number of levels of decomposition and hence synthesis.
%
%Refer to Chapter 4 for more information on biorthogonal wavelet 
%decomposition and reconstruction. 
%
%Author: Ajit S. Bopardikar
%Copyright (c) 1998 by Addison Wesley Longman, Inc.
%

num = nargin; %number of input arguments
%if the number of input arguments is 3 then use the second argument to
%pick up the filter bank and the third argument gives the number of levels
  if (num ==3)
    levs = sh;
   if(sl == 1)
     sl =[-0.17677669529664 0.17677669529664 0.70710678118655 0.70710678118655 0.17677669529664  -0.17677669529664];
     sh =[-0.70710678118655   0.70710678118655];
   elseif (sl ==2)
     sl =[0.70710678118655   0.70710678118655];
     sh =[-0.17677669529664 -0.17677669529664 0.70710678118655 -0.70710678118655 0.17677669529664 0.17677669529664];
   elseif (sl >=3)
      if (sl > 3)
       fprintf('fopt chosen to be greater than 3. Using fopt=3 instead\n');
      end; 
     sl =[-0.35355339059327 1.06066017177982 1.06066017177982 -0.35355339059327];
     sh =[-0.17677669529664 0.53033008588991 -0.53033008588991 0.17677669529664];
   end %end inner if
  end %enf if

  l = length(anal);
  
  lens = [l]; %initialization
%Now determine the lengths of each subband
  for i=1:(levs-1)
   if ( length(sh)/4 == round(length(sh)/4)) %center odd
     
     if (l/2 == round(l/2)) %length of data even
       l = l/2;
     else  %length odd
       l = (l+1)/2;
     end %end inner if

   else           %center even
  
     if (l/2 == round(l/2)) %length of data even
       l =l/2 + 1;
     else
       l = (l + 1)/2;
     end %end inner if

  end %end outer if 

  lens = [l lens]; %append the newly computed length to the list
 end %end for 
%Now begin the synthesis process
 for i=1:levs
    
    sy = anal(1:lens(i));

  if (lens(i)/2 == round(lens(i)/2) ) %even length 
    sy = bisynt2(sy,sl,sh); %One level synthesis for even length

  else  %odd length 
    
    sy = bisynt4(sy,sl,sh); %one level synthesis for odd length

  end %end if

    anal(1:lens(i)) = sy; %update the analysis array with the newly
 end %end for             %synthesized subband
  
  %plot the eventual signal
  figure;plot(sy);title('IDWT of Input DWT Array');