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.
Package: ltfat