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%-*- texinfo -*-
%@deftypefn {Function} demo_phaseplot
%@verbatim
%DEMO_PHASEPLOT Give demos of nice phaseplots
%
% This script creates a synthetic signal and then uses PHASEPLOT on it,
% using several of the possible options.
%
% For real-life signal only small parts should be analyzed. In the chosen
% demo the fundamental frequency of the speaker can be nicely seen.
%
% Figure 1: Synthetic signal
%
% Compare this to the pictures in reference 2 and 3. In
% the first two figures a synthetic signal is analyzed. It consists of a
% sinusoid, a small Delta peak, a periodic triangular function and a
% Gaussian. In the time-invariant version in the first part the periodicity
% of the sinusoid can be nicely seen also in the phase coefficients. Also
% the points of discontinuities can be seen as asymptotic lines approached
% by parabolic shapes. In the third part both properties, periodicity and
% discontinuities can be nicely seen. A comparison to the spectogram shows
% that the rectangular part in the middle of the signal can be seen by the
% phase plot, but not by the spectogram.
%
% In the frequency-invariant version, the fundamental frequency of the
% sinusoid can still be guessed as the position of an horizontal
% asymptotic line.
%
% Figure 2: Synthetic signal, thresholded.
%
% This figure shows the same as Figure 1, except that values with low
% magnitude has been removed.
%
% Figure 3: Speech signal.
%
% The figure shows a part of the 'linus' signal. The fundamental
% frequency of the speaker can be nicely seen.
%
% References:
% R. Carmona, W. Hwang, and B. Torresani. Multiridge detection and
% time-frequency reconstruction. IEEE Trans. Signal Process.,
% 47:480--492, 1999.
%
% R. Carmona, W. Hwang, and B. Torresani. Practical Time-Frequency
% Analysis: continuous wavelet and Gabor transforms, with an
% implementation in S, volume 9 of Wavelet Analysis and its Applications.
% Academic Press, San Diego, 1998.
%
% A. Grossmann, M. Holschneider, R. Kronland-Martinet, and J. Morlet.
% Detection of abrupt changes in sound signals with the help of wavelet
% transforms. Inverse Problem, pages 281--306, 1987.
%
%@end verbatim
%@strong{Url}: @url{http://ltfat.github.io/doc/demos/demo_phaseplot.html}
%@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_phaseplot" to see a description of how this demo works.');
tt=0:98;
f1=sin(2*pi*tt/33); % sinusoid
f2=zeros(1,100);
f2(50)=1; % delta-like
f3=fftshift(firwin('tria',32)).';
f4 = fftshift(pgauss(100)).';
f4 = f4/max(f4);
sig = 0.9*[f1 0 f2 f3 -f3 f3 f4 0 0 0 0];
figure(1);
sgram(sig,'lin','nf');
figure(2);
subplot(3,1,1);
plot(sig);
title('Synthetic signal');
subplot(3,1,2);
phaseplot(sig,'freqinv');
title('Phaseplot of synthetic signal - frequency-invariant phase');
subplot(3,1,3);
phaseplot(sig,'timeinv')
title('Phaseplot of synthetic signal - time-invariant phase');
figure(3);
subplot(3,1,1);
plot(sig);
title('Synthetic signal');
subplot(3,1,2);
phaseplot(sig,'freqinv','thr',0.001)
title('Phaseplot of synthetic signal - thresholded version, freq. inv. phase');
subplot(3,1,3);
phaseplot(sig,'thr',0.001)
title('Phaseplot of synthetic signal - thresholded version, time inv. phase');
figure(4);
f=linus;
f = f(4500:8000);
subplot(3,1,1);
plot(f);
axis tight;
title('Speech signal: linus');
subplot(3,1,2);
phaseplot(f)
title('Phaseplot of linus');
subplot(3,1,3);
phaseplot(f,'thr',.001)
title('Phaseplot of linus - thresholded version');
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