Function: gabdualnorm

GABDUALNORM  Measure of how close a window is to being a dual window
  Usage:  dn=gabdualnorm(g,gamma,a,M);
          dn=gabdualnorm(g,gamma,a,M,L);
          dn=gabdualnorm(g,gamma,a,M,'lt',lt);
          [scal,res]=gabdualnorm(...);

  Input parameters:
        gamma  : input window..
        g      : window function.
        a      : Length of time shift.
        M      : Number of modulations.
        L      : Length of transform to consider
  Output parameters:
        dn     : dual norm.
        scal   : Scaling factor
        res    : Residual

  GABDUALNORM(g,gamma,a,M) calculates how close gamma is to being a
  dual window of the Gabor frame with window g and parameters a and M.

  The windows g and gamma may be vectors of numerical values, text strings
  or cell arrays. See the help of GABWIN for more details.

  [scal,res]=GABDUALNORM(...) computes two entities: scal determines
  if the windows are scaled correctly, it must be 1 for the windows to be
  dual. res is close to zero if the windows (scaled correctly) are dual
  windows.

  GABDUALNORM(g,gamma,a,M,L) does the same, but considers a transform
  length of L.

  GABDUALNORM(g,gamma,a,M,'lt',lt) does the same for a non-separable
  lattice specified by lt. Please see the help of MATRIX2LATTICETYPE
  for a precise description of the parameter lt.

  GABDUALNORM can be used to get the maximum relative reconstruction
  error when using the two specified windows. Consider the following code
  for some signal f, windows g, gamma, parameters a and M and 
  transform-length L (See help on DGT on how to obtain L*):

    fr=idgt(dgt(f,g,a,M),gamma,a); 
    er=norm(f-fr)/norm(f);
    eest=gabdualnorm(g,gamma,a,M,L);

  Then  er<eest for all possible input signals f.

  To get a similar estimate for an almost tight window gt, simply use :
 
    eest=gabdualnorm(gt,gt,a,M,L);

Url: http://ltfat.github.io/doc/gabor/gabdualnorm.html

See also: gabframebounds, dgt.

Package: ltfat