Statistical performance of Wigner-Ville distribution and windowed Wigner-Ville distribution

Wigner-Ville distribution (WVD) is a major method for analyzing nonstationary signal. In practical application of WVD, a windowed version is necessary. In this paper, the statistical performance in terms of bias and variance of WVD and windowed WVD are studied. It has been shown that the WVD and the windowed WVD are biased and have the same bias. The variance of the windowed WVD is smaller than the variance of the WVD. The effects of the window type and window length on the windowed WVD are also discussed. The variance of the windowed WVD depends on the window type and window length. There is a tradeoff between the variance and the frequency resolution of the windowed WVD. It is suggested that, the window with the smallest window length should be used if the frequency resolution is satisfied.