PWVDPolynomial Wigner Ville Distribution
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Caption: Figure 13: Analysis of a received signal using the PWVD: (a) received signal at the water level of 50 mm, (b) the PWVD result in time-frequency domain, and (c) the result of PWVD at 130 kHz.
In order to build the STFD matrix, we first give the discrete form of PWVD of the signal x(t):
On the condition that the receiver is a single sensor, PWVD has always been utilized to reduce the cross-terms of Wigner-Ville distribution (WVD).
Figures 3 and 4 show the PWVD of signals received by reference sensor with L = 256 samples and the array averaged WVD in beamspace, respectively, which are both the methods utilized to reduce the cross-terms of WVD.
The most commonly used time-frequency distribution techniques are short-time Fourier transform (STFT), Wigner-Ville distribution (WVD), PWVD, and other methods.
PWVD is also using high-order multiple transform similarly.
However, other methods like HAF, PHAF or PWVD, can not appear false peaks from cross terms effect.