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function [f]=comp_idwiltiii(coef,g)
%COMP_IDWILTIII Compute Inverse discrete Wilson transform type III.
%
% This is a computational routine. Do not call it
% directly.
% AUTHOR : Peter L. Søndergaard.
% TESTING: OK
% REFERENCE: OK
M=size(coef,1);
N=size(coef,2);
W=size(coef,3);
a=M;
L=N*M;
coef2=zeros(2*M,N,W,assert_classname(coef,g));
coef2(1:2:M,1:2:N,:) = exp( i*pi/4)*coef(1:2:M,1:2:N,:);
coef2(2*M:-2:M+1,1:2:N,:) = exp(-i*pi/4)*coef(1:2:M,1:2:N,:);
coef2(1:2:M,2:2:N,:) = exp(-i*pi/4)*coef(1:2:M,2:2:N,:);
coef2(2*M:-2:M+1,2:2:N,:) = exp( i*pi/4)*coef(1:2:M,2:2:N,:);
coef2(2:2:M,1:2:N,:) = exp(-i*pi/4)*coef(2:2:M,1:2:N,:);
coef2(2*M-1:-2:M+1,1:2:N,:) = exp( i*pi/4)*coef(2:2:M,1:2:N,:);
coef2(2:2:M,2:2:N,:) = exp( i*pi/4)*coef(2:2:M,2:2:N,:);
coef2(2*M-1:-2:M+1,2:2:N,:) = exp(-i*pi/4)*coef(2:2:M,2:2:N,:);
% Apply the generalized DGT and scale.
%f=comp_igdgt(coef2,g,a,2*M,L,0,.5,0,0)/sqrt(2);
f = comp_isepdgt(coef2,g,L,a,2*M);
halfmod=exp(pi*i*(0:L-1).'/(2*M))/sqrt(2);
f=f.*repmat(halfmod,1,W);
if isreal(coef) && isreal(g)
f=real(f);
end;