function h=pconv(f,g,varargin)
%PCONV  Periodic convolution
%   Usage:  h=pconv(f,g)
%           h=pconv(f,g,ftype); 
%
%   `pconv(f,g)` computes the periodic convolution of *f* and *g*. The convolution
%   is given by
%
%   ..          L-1
%      h(l+1) = sum f(k+1) * g(l-k+1)
%               k=0
%
%   .. math:: h\left(l+1\right)=\sum_{k=0}^{L-1}f\left(k+1\right)g\left(l-k+1\right)
% 
%   `pconv(f,g,'r')` computes the convolution where *g* is reversed
%   (involuted) given by
%
%   ..          L-1
%      h(l+1) = sum f(k+1) * conj(g(k-l+1))
%               k=0
%
%   .. math:: h\left(l+1\right)=\sum_{k=0}^{L-1}f\left(k+1\right)\overline{g\left(k-l+1\right)}
%
%   This type of convolution is also known as cross-correlation.
%
%   `pconv(f,g,'rr')` computes the alternative where both *f* and *g* are
%   reversed given by
%
%   ..          L-1
%      h(l+1) = sum conj(f(-k+1)) * conj(g(k-l+1))
%               k=0
%     
%   .. math:: h\left(l+1\right)=\sum_{k=0}^{L-1}f\left(-k+1\right)g\left(l-k+1\right)
%
%   In the above formulas, $l-k$, $k-l$ and $-k$ are computed modulo $L$.
%
%   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.
%
%   See also: dft, involute

%   AUTHOR: Peter L. Søndergaard, Jordy van Velthoven
%   TESTING: TEST_PCONV
%   REFERENCE: REF_PCONV


complainif_notenoughargs(nargin, 2, 'PCONV');

definput.keyvals.L=[];
definput.keyvals.dim=[];
definput.flags.type={'default', 'r', 'rr'};
[flags,~,L,dim]=ltfatarghelper({'L','dim'},definput,varargin);

[f,~,~,Wf,dimout,permutedsize_f,order_f]=assert_sigreshape_pre(f,L,dim,'PCONV');
[g,~,~,Wg,dimout,permutedsize_g,order_g]=assert_sigreshape_pre(g,L,dim,'PCONV');

if (Wf>1) && (Wg>1)
  error('%s: Only one of the inputs can be multi-dimensional.',upper(mfilename));
end;

if size(f,1)~=size(g,1)
    error(['%s: f and g must have the same size in the direction of the',...
           ' convolution.'],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;

if isreal(f) && isreal(g)
    fftfunc = @(x) fftreal(x);
    ifftfunc = @(x) ifftreal(x, size(f,1));
else
    fftfunc = @(x) fft(x);
    ifftfunc = @(x) ifft(x);
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;
