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