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function c=ref_dwilt(f,g,a,M)
%-*- texinfo -*-
%@deftypefn {Function} ref_dwilt
%@verbatim
%REF_DWILT Reference Discrete Wilson Transform
% Usage: c=ref_dwilt(f,g,a,M);
%
% M must be even.
%@end verbatim
%@strong{Url}: @url{http://ltfat.github.io/doc/reference/ref_dwilt.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/>.
% Setup transformation matrix.
L=size(f,1);
N=L/a;
F=zeros(L,M*N);
% Zero-extend g if necessary
g=fir2long(g,L);
l=(0:L-1).';
for n=0:N/2-1
% Do the unmodulated coefficient.
F(:,2*M*n+1)=circshift(g,2*n*a);
% m odd case
for m=1:2:M-1
F(:,m+2*M*n+1) = sqrt(2)*sin(pi*m/M*l).*circshift(g,2*n*a);
F(:,m+2*M*n+M+1) = sqrt(2)*cos(pi*m/M*l).*circshift(g,(2*n+1)*a);
end;
% m even case
for m=2:2:M-1
F(:,m+2*M*n+1) = sqrt(2)*cos(pi*m/M*l).*circshift(g,2*n*a);
F(:,m+2*M*n+M+1) = sqrt(2)*sin(pi*m/M*l).*circshift(g,(2*n+1)*a);
end;
% Most modulated coefficient, Nyquest frequency.
if mod(M,2)==0
F(:,M+2*M*n+1)=(-1).^l.*circshift(g,2*n*a);
else
F(:,M+2*M*n+1)=(-1).^l.*circshift(g,(2*n+1)*a);
end;
end;
c=F'*f;
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