More on interferences: information on phase The interference terms present in any quadratic time-frequency representation, even if they disturb the readability of the representation, contain some information about the analyzed signal. The precise knowledge of their structure and construction rule is useful to interpret the information that they contain. For instance, the interference terms contain some information about the phase of a signal. Let us consider the pseudo WVD of the superposition of two constant frequency modulations, with a phase shift between the two sinusoids. If we compare the pseudo WVD for different phase shifts, we can observe a time-sliding of the oscillating interferences. The M-file movpwdph.m illustrates this property (see fig. 5.1): >> M=movpwdph(128); movie(M,10); Figure 5.1: Two simultaneous complex sinusoids analyzed by the pseudo-WVD: the position of the interferences depends on the phase-shift between the two components. These phase-shifts are respectively $\pi /4,\ 3\pi /4,\ 5\pi /4$ and $7\pi /4$ Each snapshot corresponds to the pseudo WVD with a different phase shift between the two components. A second example of signature of the phase is given by the influence of a jump of phase in a signal analyzed by the (pseudo) Wigner-Ville distribution: for instance, if we consider a constant frequency modulation presenting a jump of phase in its middle (see fig. 5.2): >> M=movpwjph(128,'C'); movie(M,10); Figure 5.2: Complex sinusoid presenting a jump of phase in its middle, analyzed by the pseudo-WVD : the shape of the PWVD-pattern changes with the importance of the jump. These jumps of phase are respectively $\pi /4,\ \pi /2,\ 3\pi /4$ and $pi$ the pseudo WVD presents a pattern around the jump position which is all the more important since this jump of phase is close to $pi$. This characteristic can be used to detect a jump of phase in a signal.
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