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function [coef]=ref_dwilt_1(f,g,a,M)
%-*- texinfo -*-
%@deftypefn {Function} ref_dwilt_1
%@verbatim
%COMP_DWILT Compute Discrete Wilson transform by DGT
%
%@end verbatim
%@strong{Url}: @url{http://ltfat.github.io/doc/reference/ref_dwilt_1.html}
%@end deftypefn
% Copyright (C) 2005-2016 Peter L. Soendergaard <peter@sonderport.dk>.
% This file is part of LTFAT version 2.2.0
%
% This program is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program. If not, see <http://www.gnu.org/licenses/>.
L=size(g,1);
N=L/a;
W=size(f,2);
coef2=dgt(f,g,a,2*M);
coef=zeros(2*M,N/2,W);
if 1
% Loop version
for n=0:N/2-1
% ---- m is zero ---------
coef(1,n+1,:)=coef2(1,2*n+1,:);
for m=1:2:M-1
% --- m is odd ----------
coef(m+1,n+1,:)= i/sqrt(2)*(coef2(m+1,2*n+1,:)-coef2(2*M-m+1,2*n+1,:));
coef(M+m+1,n+1,:)=1/sqrt(2)*(coef2(m+1,2*n+2,:)+coef2(2*M-m+1,2*n+2,:));
end;
for m=2:2:M-1
% --- m is even ---------
coef(m+1,n+1,:)= 1/sqrt(2)*(coef2(m+1,2*n+1,:)+coef2(2*M-m+1,2*n+1,:));
coef(M+m+1,n+1,:)=i/sqrt(2)*(coef2(m+1,2*n+2,:)-coef2(2*M-m+1,2*n+2,:));
end;
% --- m is nyquest ------
if mod(M,2)==0
coef(M+1,n+1,:) = coef2(M+1,2*n+1,:);
else
coef(M+1,n+1,:) = coef2(M+1,2*n+2,:);
end;
end;
else
% Vector version
% ---- m is zero ---------
coef(1,:,:)=coef2(1,2*n+1,:);
% --- m is odd ----------
% sine, first column.
coef(2:2:M,:,:)=1/sqrt(2)*i*(coef2(2:2:M,1:2:N,:)-coef2(2*M:-2:M+2,1:2:N,:));
% cosine, second column
coef(M+2:2:2*M,:,:)=1/sqrt(2)*(coef2(2:2:M,2:2:N,:)+coef2(2*M:-2:M+2,2:2:N,:));
% --- m is even ---------
% cosine, first column.
coef(3:2:M,:,:)=1/sqrt(2)*(coef2(3:2:M,1:2:N,:)+coef2(2*M-1:-2:M+2,1:2:N,:));
% sine, second column
coef(M+3:2:2*M,:,:)=1/sqrt(2)*i*(coef2(3:2:M,2:2:N,:)-coef2(2*M-1:-2:M+2,2:2:N,:));
% --- m is nyquest ------
if mod(M,2)==0
coef(M+1,:,:) = coef2(M+1,1:2:N,:);
else
coef(M+1,:,:) = coef2(M+1,2:2:N,:);
end;
end;
coef=reshape(coef,M*N,W);
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