A resolution comparison of several time-frequency representations

Cross-terms lie between two auto-components and are oscillatory, with their frequencies increasing with increasing distance in time-frequency between the two components. The cross-terms can have a peak value as high as twice that of the auto-components. A Wigner distribution of a two-component signal is shown in Figure 1. In this figure, it is easy to separate the auto-components from the cross-components, but with more complicated signals it is often extremely difficult to interpret the Wigner distribution. In an effort to combat cross-terms, several filtered variants of the Wigner distribution have been developed. Since crossterms have oscillations of relacively high frequencies, low-pass filtering can potentially reduce them, at the expense of autocomponent broadening. It is generally accepted that some smoothing of the Wigner distribution is necessary in practical time-frequency analyses. The pseudo-Wigner distribution (PWD), defined here as WD,,+y(t,w) = WD,,(t,w) + 2Re[WD",y(t,w)] + WDy(t,w) (2) has a ~cross-termn 2&[ WD",y] in addition to the two autocomponents, where the cross-Wigner distribution is denned