function transf=dec1D_pe(fp,flt,maxlevel) 
%transf=dec1D_pe(fp,flt,maxlevel) 
% 
%  This function computes discrete multiwavelet transform of a preprocessed  
%  1-dimensional signal. Boundaries are handled by periodic extension. 
%  For description of the algorithm see [SW]. 
% 

% 
%  Input:   
%    maxlevel    integer, number of levels of decomposition 
%    flt         string of characters, name of the filter; 
%                for possible names and short descriptions see coef.m 
%    fp          r by n real array, preprocessed input data; 
%                r is the number of scaling functions,    
%                n must be of the form integer*2^maxlevel 
% 
%  Output: 
%    transf      r by n real array, multiscaling and multiwavelet coefficients; 
%                transf is organized as follows:    
%                columns 1 to n/2^maxlevel -- multiscaling coefficients 
%                columns n/2^maxlevel +1 to n/2^(maxlevel-1) -- coarsest  
%                   multiwavelet coefficients  
%                            ........................   
%                columns n/2+1 to n -- finest multiwavelet coefficient 
% 
%  Example of Usage: 
%   transf=dec1D_pe(fp,'cl',5)  
 
 
n=length(fp(1,:)); 
 
[L,H]=coef(flt); 
[nf,ns]=size(L); 
[nf,nw]=size(H); 
ns=ns/nf;  
nw=nw/nf; 
if ns < nw 
  big=nw; 
else 
  big=ns; 
end 
if fix(big/2) ~= big/2 
  big=(big+1)/2; 
else 
  big=big/2; 
end 
 
i=1; 
nss=1; 
while L(:,nf*(i-1)+1:nf*i)==zeros(nf) 
  nss=nss+1; 
  i=i+1; 
end 
i=1; 
nws=1; 
while H(:,nf*(i-1)+1:nf*i)==zeros(nf) 
  nws=nws+1; 
  i=i+1; 
end 
 
transf=fp; 
for lv=1:maxlevel 
  fp=zeros(nf,n); 
  fp=transf(:,1:n); 
  tr=zeros(nf,n); 
  for i=1:n/2-big 
    for j=nss:ns 
      tr(:,i)=tr(:,i)+L(:,nf*(j-1)+1:nf*j)*fp(:,2*i-2+j); 
    end 
    for j=nws:nw 
      tr(:,i+n/2)=tr(:,i+n/2)+H(:,nf*(j-1)+1:nf*j)*fp(:,2*i-2+j); 
    end 
  end 
 
  for i=n/2-big+1:n/2 
    for j=nss:ns 
      if 2*i-2+j>n 
        tr(:,i)=tr(:,i)+L(:,nf*(j-1)+1:nf*j)*fp(:,2*i-2+j-n); 
      else 
        tr(:,i)=tr(:,i)+L(:,nf*(j-1)+1:nf*j)*fp(:,2*i-2+j); 
      end 
    end 
    for j=nws:nw 
      if 2*i-2+j>n 
        tr(:,i+n/2)=tr(:,i+n/2)+H(:,nf*(j-1)+1:nf*j)*fp(:,2*i-2+j-n); 
      else 
        tr(:,i+n/2)=tr(:,i+n/2)+H(:,nf*(j-1)+1:nf*j)*fp(:,2*i-2+j); 
      end 
    end 
  end 
  transf(:,1:n)=tr; 
  n=n/2; 
end