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%-*- texinfo -*-
%@deftypefn {Function} demo_nsdgt
%@verbatim
%DEMO_NSDGT Non-stationary Gabor transform demo
%
% This script sets up a non-stationary Gabor frame with the specified
% parameters, computes windows and corresponding canonical dual windows
% and a test signal, and plots the windows and the energy of the
% coefficients.
%
% Figure 1: Windows + dual windows
%
% This figure shows the window functions used and the corresponding
% canonical dual windows.
%
% Figure 2: Spectrogram (absolute value of coefficients in dB)
%
% This figure shows a (colour-coded) image of the nsdgt coefficient
% modulus.
%
%@end verbatim
%@strong{Url}: @url{http://ltfat.github.io/doc/demos/demo_nsdgt.html}
%@seealso{nsdgt, insdgt, nsgabdual}
%@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_nsdgt" to see a description of how this example',...
' works.']);
% Setup parameters and length of signal.
Ls=965; % Length of signal.
N=16; % Number of time positions
% Define a set of windows with length growing linearly. The step beetween
% to consecutive windows also grows linearly.
M=round(linspace(40,200,N)');
a=cumsum(round(M/2));
a=a-a(1);
a_new=round(M/2);
g={};
for ii=1:length(M)
g{ii}=firwin('hann',M(ii));
end
% Compute corresponding dual windows
gd=nsgabdual(g,a_new,M,Ls);
% Plot them
figure(1);
color = ['b', 'r'];
for ii = 1:length(a)
subplot(2,1,1);
hold on;
plot(a(ii)-1-floor(M(ii)/2)+(1:M(ii)), fftshift(g{ii}),...
color(rem(ii,2)+1));
subplot(2,1,2);
hold on;
plot(a(ii)-1-floor(M(ii)/2)+(1:M(ii)), fftshift(gd{ii}),...
color(rem(ii,2)+1));
end
subplot(2,1,1);
title('Analysis windows');
xlabel('Time index');
subplot(2,1,2);
title('Dual synthesis windows');
xlabel('Time index');
% Define a sinus test signal so it is periodic.
f=sin(2*pi*(289/Ls)*(0:Ls-1)');
% Calculate coefficients.
c=nsdgt(f,g,a_new,M);
% Plot corresponding spectrogram
figure(2);
plotnsdgt(c,a,'dynrange',100);
title('Spectrogram of test signal')
% Test reconstruction
f_r=insdgt(c,gd,a_new,Ls);
% Print relative error of reconstruction.
rec_err = norm(f-f_r)/norm(f);
fprintf(['Relative error of reconstruction (should be close to zero.):'...
' %e \n'],rec_err);
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