candual.m

linear time－frequency toolbox

function gamma=candual(g,a,M,L)
%CANDUAL  Canonical dual window.
%   Usage:  gamma=candual(g,a,M);
%           gamma=candual(g,a,M,L);
%
%   Input parameters:
%         g     : Gabor window.
%         a     : Length of time shift.
%         M     : Number of channels.
%         L     : Length of window. (optional)
%   Output parameters:
%         gamma : Canonical dual window.
%
%   CANDUAL(g,a,M) computes the canonical dual window of the discrete
%   Gabor frame with window g and parameters a, M.
%
%   If L is specified, then the window will be padded or truncated to
%   length L before the canonical dual window is calculated. gamma
%   will also have length L.
%
%   If a>M then the dual window of the Gabor Riesz sequence with window g
%   and parameters a and M will be calculated.
%
%   SEE ALSO:  CANTIGHT, ISNORMALFORM

error(nargchk(3,4,nargin));

if size(g,1)*size(g,2)==1
  error('g must be a vector (you probably forgot to supply the window function as input parameter.)')
end;

wasrow=0;
if size(g,2)>1
  if size(g,1)>1
    error('g must be a vector');
  else
    % g was a row vector.
    g=g(:);
    wasrow=1;
  end;
end;

assert_squarelat(a,M,1,'CANDUAL',0);

Lwindow=length(g);
Ls=Lwindow;

if nargin<4
  [b,N,L]=assert_L(-Ls,Lwindow,a,M,'CANDUAL');
else
  [b,N,L]=assert_L(L,Lwindow,a,M,'CANDUAL');
  g=firextend(g,L);
end;

  
% If input is real, output must be real as well.
inputwasreal = isreal(g);

if a>M

  % Handle the Riesz basis (dual lattice) case.

  gf=comp_wfac(g,M,a);
  gammaf=comp_candual_fac(gf,L,M,a)*a/M;
  gamma=comp_iwfac(gammaf,L,M,a);
  
else

  % Handle the frame case

  gf=comp_wfac(g,a,M);
  gammaf=comp_candual_fac(gf,L,a,M);
  gamma=comp_iwfac(gammaf,L,a,M);

  

end;
  

if inputwasreal
  gamma=real(gamma);
end;
      
if wasrow
  gamma=gamma.';
end;