Bias error due to windows for the Wigner–Ville distribution estimation

Abstract

The Wigner–Ville distribution has been recognized as a useful method for time-frequency analysis of non-stationary signals. For mechanical signatures such as vibration and acoustic signals it has demonstrated a very good ability to reveal what actually happens, which is not the case if the signals are processed by conventional methods such as spectrum analysis and amplitude-time analysis. Because of these promising figures for the Wigner–Ville interpretation of mechanical signatures, the possible errors associated with estimation, which are mainly due to the finite record length, have not been analysed. In this paper, the error due to the time window which changes with respect to time, and the error associated with the smoothing process have been analysed theoretically. The error produced by employing a time window has been found to be proportional to the frequency of curvature of the Wigner–Ville distribution and that associated with smoothing has turned out to be proportional to even numbers of derivatives with respect to time and frequency.