This function makes a synthesis of a path in a filter bank, for each pixel
  of datapack DATA. 

  It uses in cascade of reconstruction blocks Bi with i=1 to i=L=length(SEQ). 
  Each reconstruction block Bi is formed by:
  1) up-sampler by 2
  2) gain of 2
  3) Gj FIR FILTER, so that j=SEQ(L+1-i)

  The function accepts the filter H0 as input parameter, so that the filters 
  G0 and G1  are calculated as $G0[Z]=H0[Z]$ and $G1[Z]= -H0[-Z]$.
  If
  H0    = [h0 h1 h2 ... h(M-1)]
  then your Z transform is:
  M2=floor(M/2);
  $H[Z] = h0 Z^{+M2} + h1 Z^{+M2-1} + ...  h(M-1) Z^{+M2-(M-1)}$ 
 
  H0 should be a low pass FIR filter with cut-off in pi/2 
  (for a 2*pi normalized frequency range).
  In order to get a perfect reconstruction it is necessary that 
  $D[Z]=H0^2[Z]-H0^2[-Z]=A Z^C$ for any A and C.

  
  After starting the main routine just type the following command at the
  prompt:
  DATAOUT=firsynthesispath(DATA,H0,SEQ);
  
  Input:
  DATA   is a speckle data pack. Where DATA is a 3D matrix created grouping NTIMES 
         intensity matrices with NLIN lines and NCOL columns. When N=size(DATA0), then
         N(1,1) represents NLIN and
         N(1,2) represents NCOL and
         N(1,3) represents NTIMES.
         DATA is obtained after the down-sampler of output of H0 FIR filter in 
         a step of a filter bank with low-pass filter H0.
  H0     is a vector with the parameters of a FIR filter. H0 should be a low 
         pass filter with cut-off in pi/2 (for a 2*pi normalized frequency range).
         In order to get a perfect reconstruction is necessary that 
         $D[Z]=H0^2[Z]-H0^2[-Z]=A Z^B$ for any A and B.
  SEQ    is a vector with binary values. These values indicates the path
         in the decomposition scheme used to get the datapack DATA.
  
  Output:
  DATAOUT is a synthesis of the speckle datapack DATA. The number of images
          inside DATAOUT is 2^{L=length(SEQ)} times of the number of images of DATA.
  

  For help, bug reports and feature suggestions, please visit:
  http://nongnu.org/bsltl/

Package: bsltl