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%-*- texinfo -*-
%@deftypefn {Function} demo_gabmixdual
%@verbatim
%DEMO_GABMIXDUAL How to use GABMIXDUAL
%
% This script illustrates how one can produce dual windows
% using GABMIXDUAL
%
% The demo constructs a dual window that is more concentrated in
% the time domain by mixing the original Gabor window by one that is
% extremely well concentrated. The result is somewhat in the middle
% of these two.
%
% The lower framebound of the mixing Gabor system is horrible,
% but this does not carry over to the gabmixdual.
%
% Figure 1: Gabmixdual of two Gaussians.
%
% The first row of the figure shows the canonical dual window
% of the input window, which is a Gaussian function perfectly
% localized in the time and frequency domains.
%
% The second row shows the canonical dual window of the window we
% will be mixing with: This is a Gaussian that is 10 times more
% concentrated in the time domain than in the frequency domain.
% The resulting canonical dual window has rapid decay in the time domain.
%
% The last row shows the gabmixdual of these two. This is a non-canonical
% dual window of the first Gaussian, with decay resembling that of the
% second.
%
%@end verbatim
%@strong{Url}: @url{http://ltfat.github.io/doc/demos/demo_gabmixdual.html}
%@seealso{gabmixdual, gabdual}
%@end deftypefn
% Copyright (C) 2005-2016 Peter L. Soendergaard <peter@sonderport.dk>.
% This file is part of LTFAT version 2.3.1
%
% This program is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program. If not, see <http://www.gnu.org/licenses/>.
disp('Type "help demo_gabmixdual" to see a description of how this demo works.');
L=120;
a=10;
M=12;
% Compute frequency shift.
b=L/M;
% Optimally centered Gaussian
g1=pgauss(L);
% Compute and print framebounds.
[A1,B1]=gabframebounds(g1,a,M);
disp('');
disp('Framebounds of initial Gabor system:');
A1, B1
% Narrow Gaussian
g2=pgauss(L,.1);
% Compute and print framebounds.
[A2,B2]=gabframebounds(g2,a,M);
disp('');
disp('Framebounds of mixing Gabor system:');
A2, B2
% Create a gabmixdual. The window gd is a dual window to g1
gd=gabmixdual(g1,g2,a,M);
% Compute and print framebounds.
[Am,Bm]=gabframebounds(gd,a,M);
disp('');
disp('Framebounds of gabmixdual Gabor system:');
Am, Bm
% Create canonical duals, for plotting.
gc1=gabdual(g1,a,M);
gc2=gabdual(g2,a,M);
% Standard note on plotting:
%
% - The windows are all centered around zero, but this
% is not visually pleasing, so the window must be
% shifted to the middle by an FFTSHIFT
figure(1);
subplot(3,2,1);
plot(fftshift(gc1));
title('Canonical dual window.');
subplot(3,2,2);
plot(20*log10(abs(fftshift(gc1))));
title('Decay of canonical dual window.');
subplot(3,2,3);
plot(fftshift(gc2));
title('Can. dual of mix. window.');
subplot(3,2,4);
plot(20*log10(abs(fftshift(gc2))));
title('Decay of can.dual of mix. window.')
subplot(3,2,5);
plot(fftshift(gd));
title('Gabmixdual');
subplot(3,2,6);
plot(20*log10(abs(fftshift(gd))));
title('Decay of gabmixdual');
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