examp_phaseplot.m

linear time－frequency toolbox

%EXAMP_PHASEPLOT  Give examples 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 
%   example 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 phaselocked 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 not phase-locked version still the fundamental frequency of the 
%     sinusoid can 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. Torrésani. Multiridge detection and
%     time-frequency reconstruction. IEEE Trans. Signal Process., 47:480-492,
%     1999.
%     
%     R. Carmona, W. Hwang, and B. Torrésani. 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.

disp('Type "help examp_phaseplot" to see a description of how this example works.');

tt=0:98;
f1=sin(2*pi*tt/33); % sinusoid

f2=zeros(1,100);
f2(50)=1; % delta-like

f3=triang(33).';

f4 = fftshift(pgauss(100)).';
f4 = f4/max(f4);

sig = 0.9*[f1 0 f2 f3 -f3 f3 f4];

figure(1);
subplot(3,1,1);
plot(sig);
title('Synthetic signal');
legend('off');

subplot(3,1,2);
phaseplot(sig); 
title('Phaseplot of synthetic signal - standard version');

subplot(3,1,3);
phaseplot(sig,'phl')
title('Phaseplot of synthetic signal - phaselocked version');
colormap(jet);

figure(2);
subplot(3,1,1);
plot(sig);
title('Synthetic signal');
legend('off');

subplot(3,1,2);
phaseplot(sig,'thr')
title('Phaseplot of synthetic signal - threshold version');

subplot(3,1,3);
phaseplot(sig,'phl','thr')
title('Phaseplot of synthetic signal - phaselocked and threshold version');
colormap(jet);

figure(3);
f=linus();
f = f(4500:8000);

subplot(3,1,1);
plot(f);
axis tight;
title('Speech signal: linus');
legend('off');

subplot(3,1,2);
phaseplot(f,'phl')
title('Phaseplot of linus - phaselocked version');

subplot(3,1,3);
phaseplot(f,'phl','thr')
title('Phaseplot of linus - phaselocked and threshold version');
colormap(jet);