function f=idft(c,N,dim)
%IDFT Inverse normalized Discrete Fourier Transform
% Usage: f=idft(c);
% f=idft(c,N,dim);
%
% IDFT computes a normalized or unitary inverse discrete Fourier transform.
% The unitary discrete Fourier transform is computed by
%
% L-1
% f(l+1) = 1/sqrt(L) * sum c(k+1)*exp(2*pi*i*k*l/L)
% k=0
%
% for l=0,...,L-1.
%
% The output of IDFT is a scaled version of the output from ifft. The
% function takes exactly the same arguments as ifft. See the help on ifft
% for a thorough description.
%
% See also: dft
%
% Url: http://ltfat.github.io/doc/fourier/idft.html
% Copyright (C) 2005-2023 Peter L. Soendergaard <peter@sonderport.dk> and others.
% This file is part of LTFAT version 2.6.0
%
% 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/>.
% AUTHOR: Peter L. Søndergaard, Jordy van Velthoven
% TESTING: TEST_IDFT
% REFERENCE: TEST_DFT
complainif_argnonotinrange(nargin,1,3,mfilename);
if nargin<3
dim=[];
end;
if nargin<2
N=[];
end;
[c,N,Ls,W,dim,permutedsize,order]=assert_sigreshape_pre(c,N,dim,'IDFT');
% Force IFFT along dimension 1, since we have permuted the dimensions
% manually
f=ifft(c,N,1)*sqrt(N);
f=assert_sigreshape_post(f,dim,permutedsize,order);