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function [g]=comp_pgauss(L,w,c_t,c_f)
%-*- texinfo -*-
%@deftypefn {Function} comp_pgauss
%@verbatim
%COMP_PGAUSS Sampled, periodized Gaussian.
%
% Computational routine: See help on PGAUSS.
%
% center=0 gives whole-point centered function.
% center=.5 gives half-point centered function.
%
% Does not check input parameters, do not call this
% function directly.
%@end verbatim
%@strong{Url}: @url{http://ltfat.github.io/doc/comp/comp_pgauss.html}
%@end deftypefn
% Copyright (C) 2005-2016 Peter L. Soendergaard <peter@sonderport.dk>.
% This file is part of LTFAT version 2.3.1
%
% 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. Soendergaard.
% AUTHOR : Peter L. Soendergaard.
% TESTING: OK
% REFERENCE: OK
% c_t - time centering
% c_f - frequency centering
% Input data type cannot be determined
g=zeros(L,1);
if L==0
return;
end;
sqrtl=sqrt(L);
safe=4;
% Keep the delay in a sane interval
c_t=rem(c_t,L);
% Outside the interval [-safe,safe] then exp(-pi*x.^2) is numerically zero.
nk=ceil(safe/sqrt(L/sqrt(w)));
lr=(0:L-1).'+c_t;
for k=-nk:nk
g=g+exp(-pi*(lr/sqrtl-k*sqrtl).^2/w+2*pi*i*c_f*(lr/L-k));
end;
% Normalize it exactly.
g=g/norm(g);
% This normalization is only approximate, it works for the continous case
% but not for the discrete
%g=g*(w*L/2)^(-.25);
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