pconv.m

linear time－frequency toolbox

function h=pconv(f,g,ctype)
%PCONV  Periodic convolution
%   Usage:  h=pconv(f,g)
%           h=pconv(ptype,f,g); 
%
%   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
% 
%   PCONV('r',f,g) computes the alternative where g is reversed given by
% 
%               L-1
%      h(l+1) = sum f(k+1) * conj(g(k-l+1))
%               k=0
% 
%   PCONV('rr',f,g) 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
%      
%   In the above formulas, l-k, k-l and -k are computed modulo L.
%
%   SEE ALSO: DFT, INVOLUTE

% AUTHOR: Peter Soendergaard

if nargin==2
  ctype='';
end;

switch(lower(ctype))
  case {''}
    h=ifft(fft(f).*fft(g));
  case {'r'}
    h=ifft(fft(f).*conj(fft(g)));
  case {'rr'}
    h=ifft(conj(fft(f)).*conj(fft(g)));
end;

% Clean output if input was real-valued
if isreal(f) && isreal(g)
  h=real(h);
end;