cantight.m

linear time－frequency toolbox

function gamma=cantight(p1,p2,p3,p4)
%CANTIGHT  Canonical tight window.
%   Usage:  gamma=cantight(a,M,L);
%           gamma=cantight(g,a,M);
%           gamma=cantight(g,a,M,L);
%
%   Input parameters:
%         g     : Gabor window.
%         a     : Length of time shift.
%         M     : Number of modulations.
%         L     : Length of window. (optional)
%   Output parameters:
%         gamma : Canonical tight window, column vector.
%
%   CANTIGHT(a,M,L) computes a nice tight window of length L for a
%   lattice with parameters a, M.
%
%   CANTIGHT(g,a,M) computes the canonical tight window of the Gabor
%   frame with window g and parameters a, M.
%
%   CANTIGHT(g,a,M,L) pads or truncates g to length L before
%   calculating the tight window. gamma will also be of length L.
%
%   If a>M then an orthonormal window of the Gabor Riesz sequence with
%   window g and parameters a and M will be calculated.
%
%   SEE ALSO:  CANDUAL

%   Author : Peter Soendergaard.

wasrow=0;

if nargin<3
  error('Too few input parameters.');
end;

if nargin>4
  error('Too many input parameters.');
end;

wasrow=0;
if prod(size(p1))==1
  % First argument is a scalar.
    
  % Type 1: Nice tight win for sep system.

  a=p1;
  M=p2;
  L=p3;

  assert_squarelat(a,M,1,'CANTIGHT',0);
  [b,N,L]=assert_L(L,L,a,M,'CANTIGHT');

  % Create default window, a Gaussian.
  g=comp_pgauss(L,a/b,0);

else
  % First argument assumed to be a vector.
  
  g=p1;
  L=length(g); % might be overwritten later.
  
  % Take care of row/column preferences. Convert to column layout.
  if size(g,1)==1
    wasrow=1;
    % Make g a column vector.
    g=g(:);
  end;
  
  if size(p2,1)*size(p2,2)==1
    % Second argument a scalar.
    
    if nargin<3
      error('To few input parameters.');
    end;
    
    a=p2;
    M=p3;
    
    assert_squarelat(a,M,1,'CANTIGHT',0);

    Lwindow=length(g);
    Ls=Lwindow;

    if nargin<4
      [b,N,L]=assert_L(-Ls,Lwindow,a,M,'CANTIGHT');
    else
      [b,N,L]=assert_squarelat(L,Lwindow,a,M,'CANTIGHT');
      g=firextend(g,L);
    end;
       
  end;
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_cantight_fac(gf,L,M,a)*sqrt(a/M);
  gamma=comp_iwfac(gammaf,L,M,a);
  
else

  % Handle the frame case

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

end;

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