function [coef2]=comp_idwiltiv(coef,a,M)
%COMP_IDWILTIV  Compute Inverse discrete Wilson transform type IV.
% 
%   This is a computational routine. Do not call it
%   directly.
%
%   Url: http://ltfat.github.io/doc/comp/comp_idwiltiv.html

% Copyright (C) 2005-2015 Peter L. Soendergaard <peter@sonderport.dk>.
% This file is part of LTFAT version 2.1.1
%
% 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/>.

%   AUTHOR : Peter L. Søndergaard

N=size(coef,1)/M;
W=size(coef,2);
L=N*a;

coef=reshape(coef,M,N,W);

coef2=zeros(2*M,N,W,assert_classname(coef));

coef2(1:2:M,1:2:N,:)        = exp(i*pi/4)/sqrt(2)*coef(1:2:M,1:2:N,:);
coef2(2*M:-2:M+1,1:2:N,:)   = exp(i*pi*3/4)/sqrt(2)*coef(1:2:M,1:2:N,:);

coef2(1:2:M,2:2:N,:)        = exp(-i*pi/4)/sqrt(2)*coef(1:2:M,2:2:N,:);
coef2(2*M:-2:M+1,2:2:N,:)   = exp(-i*pi*3/4)/sqrt(2)*coef(1:2:M,2:2:N,:);

coef2(2:2:M,1:2:N,:)        = exp(-i*pi/4)/sqrt(2)*coef(2:2:M,1:2:N,:);
coef2(2*M-1:-2:M+1,1:2:N,:) = exp(-i*pi*3/4)/sqrt(2)*coef(2:2:M,1:2:N,:);

coef2(2:2:M,2:2:N,:)        = exp(i*pi/4)/sqrt(2)*coef(2:2:M,2:2:N,:);
coef2(2*M-1:-2:M+1,2:2:N,:) = exp(i*pi*3/4)/sqrt(2)*coef(2:2:M,2:2:N,:);



