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function h=lconv(f,g,varargin)
%-*- texinfo -*-
%@deftypefn {Function} lconv
%@verbatim
%LCONV Linear convolution
% Usage: h=lconv(f,g);
%
% LCONV(f,g) computes the linear convolution of f and g. The linear
% convolution is given by
%
% Lh-1
% h(l+1) = sum f(k+1) * g(l-k+1)
% k=0
%
% with L_{h} = L_{f} + L_{g} - 1 where L_{f} and L_{g} are the lengths of f and g,
% respectively.
%
% LCONV(f,g,'r') computes the linear convolution of f and g where g is reversed.
% This type of convolution is also known as linear cross-correlation and is given by
%
% Lh-1
% h(l+1) = sum f(k+1) * conj(g(k-l+1))
% k=0
%
% LCONV(f,g,'rr') computes the alternative where both f and g are
% reversed given by
%
% Lh-1
% h(l+1) = sum conj(f(-k+1)) * conj(g(k-l+1))
% k=0
%
% In the above formulas, l-k, k-l and -k are computed modulo L_{h}.
%
% The input arrays f and g can be 1D vectors or one of them can be
% a multidimensional array. In either case, the convolution is performed
% along columns with row vectors transformed to columns.
%
%@end verbatim
%@strong{Url}: @url{http://ltfat.github.io/doc/fourier/lconv.html}
%@seealso{pconv}
%@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/>.
% AUTHOR: Jordy van Velthoven
% TESTING: TEST_LCONV
% REFERENCE: REF_LCONV
complainif_notenoughargs(nargin, 2, 'LCONV');
definput.keyvals.L=[];
definput.keyvals.dim=[];
definput.flags.type={'default', 'r', 'rr'};
[flags,~,L,dim]=ltfatarghelper({'L','dim'},definput,varargin);
[f,~,Lf,Wf,dimoutf,permutedsize_f,order_f]=assert_sigreshape_pre(f,L,dim,'LCONV');
[g,~,Lg,Wg,dimoutg,permutedsize_g,order_g]=assert_sigreshape_pre(g,L,dim,'LCONV');
if (Wf>1) && (Wg>1)
error('%s: Only one of the inputs can be multi-dimensional.',upper(mfilename));
end;
W=max(Wf,Wg);
if Wf<W
f=repmat(f,1,W);
end;
if Wg<W
g=repmat(g,1,W);
end;
Lh = Lf+Lg-1;
f = postpad(f,Lh);
g = postpad(g,Lh);
if isreal(f) && isreal(g)
fftfunc = @(x) fftreal(x);
ifftfunc = @(x) ifftreal(x, Lh);
else
fftfunc = @(x) fft(x);
ifftfunc = @(x) ifft(x, Lh);
end;
if flags.do_default
h=ifftfunc(fftfunc(f).*fftfunc(g));
end;
if flags.do_r
h=ifftfunc(fftfunc(f).*(conj(fftfunc(g))));
end;
if flags.do_rr
h=ifftfunc((conj(fftfunc(f))).*(conj(fftfunc(g))));
end;
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