Function: gabtight
GABTIGHT  Canonical tight window of Gabor frame
  Usage:  gt=gabtight(a,M,L);
          gt=gabtight(g,a,M);
          gt=gabtight(g,a,M,L);
          gd=gabtight(g,a,M,'lt',lt);

  Input parameters:
        g     : Gabor window.
        a     : Length of time shift.
        M     : Number of modulations.
        L     : Length of window. (optional)
        lt    : Lattice type (for non-separable lattices).
  Output parameters:
        gt    : Canonical tight window, column vector.

  GABTIGHT(a,M,L) computes a nice tight window of length L for a
  lattice with parameters a, M. The window is not an FIR window,
  meaning that it will only generate a tight system if the system
  length is equal to L.

  GABTIGHT(g,a,M) computes the canonical tight window of the Gabor frame
  with window g and parameters a, M.

  The window g may be a vector of numerical values, a text string or a
  cell array. See the help of GABWIN for more details.
 
  If the length of g is equal to M, then the input window is assumed to
  be a FIR window. In this case, the canonical dual window also has
  length of M. Otherwise the smallest possible transform length is
  chosen as the window length.

  GABTIGHT(g,a,M,L) returns a window that is tight for a system of
  length L. Unless the input window g is a FIR window, the returned
  tight window will have length L.

  GABTIGHT(g,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.

  If a>M then an orthonormal window of the Gabor Riesz sequence with
  window g and parameters a and M will be calculated.

  Examples:
  ---------

  The following example shows the canonical tight window of the Gaussian
  window. This is calculated by default by GABTIGHT if no window is
  specified:

    a=20;
    M=30;
    L=300;
    gt=gabtight(a,M,L);
    
    % Simple plot in the time-domain
    figure(1);
    plot(gt);

    % Frequency domain
    figure(2);
    magresp(gt,'dynrange',100);

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

See also: gabdual, gabwin, fir2long, dgt.

Package: ltfat