• Journal of KSNVE
• /
• v.7 no.5
• /
• pp.747-756
• /
• 1997

Wigner-Ville distribution which is a time-frequency analysis has a fatal drawback, when the signal has multiple components. This is the cross-talk and often causes a neagative value in the distribution. Wingner-Ville distriution is an expression of power, therefore the cross-talk must be avoided. Smoothing the Wigner-Ville distribution by convoluting it with a window, is most commonly used to reduce the cross-talk. There can be infinite number of distributions depending on the windows. But, the smoothing reduces resolution in time-frequency plane; this motives to design a more effective window in reducing cross-talk while remaining resolution. The domain in which the cross-talk and legitimate components can be easily distinguished, is the ambiguity function. In the ambiguity function domain, the legitimate components appear as linear lines passing through the orgine. But, the cross-talk is widely distributes in the ambiguity function plane. Based on the relative distributions of cross-talk and legitimate components, rotating window can be designed to minimize cross-talk. Applying the rotating window to the ambiguity function corresponds to smoothing the Wigner-Ville distribution. Therefore, the effects of rotating window is estimated in terms of the bias error due to smooting the Wigner-Ville distribution. By applying the rotating window, not only the Wigner-Ville distribution but also its properties are changed. The properties of the new distribution are checked, in order to complete analyzing the rotating window.

• Journal of KSNVE
• /
• v.7 no.2
• /
• pp.319-329
• /
• 1997

Wigner-Ville distribution has been recognized as a useful tool and applied to various types of mechanical noise and vibration signals, but its limitation which mainly comes from the cross-talk has not been well addressed. The cross-talk takes place for a signal with multiple components, simply because the Wigner-Ville distribution is a bilinear transform. The cross-talk often causes a negative value in the distribution. This cannot be accepted for the Wigner- Ville distribution, because it is an expression of power. Smoothing the Wigner-Ville distribution by convoluting it wih a window, is most commonly used to reduce the cross-talk. There can be infinite number of distributions depending on the windows. In this paper, we attempted to develop a distribution which is the best or the optimal in reducing the cross-talk. This could be possible by employing the ambiguity function. For a general signal, however it is difficult to express the ambiguity function as a mathematically closed form. This requires an appropriate modeling to make such expression possible. We approximated the Wigner-Ville distribution as a sum of linear segments. In the ambiguity function domain, the legitimate components are reflected as linear lines passing through the origin. Every lines has its own length and slope. But, the cross-talk is widely distributed in the ambiguity function plane. Based on this realization, we proposed a two-dimensional window which is in fact 'rotating window', that can eliminate cross-talk component. The rotating window is examined numerically and is found to have a better performance in reducing the cross-talk than conventional windows, the Gaussian window.