Robust polynomial Wigner-Ville distribution for the analysis of polynomial phase signals in α-stable noise

The polynomial Wigner-Ville distribution (PWVD) is the most suitable time-frequency representation (TFR) of non-stationary signals which can be modelled by polynomial phase signals. It is a very efficient signal analysis tool in the case of both additive and multiplicative Gaussian noise. However, in many real life applications, noise can be non-Gaussian. Hence the PWVD fails to produce satisfactory results. On the other hand, it is well known that fractional lower-order statistics (FLOS) are signal processing tools that tend to resist outliers observed in signals. We propose a new robust FLOS-based polynomial Wigner-Ville distribution which we call the fractional lower-order polynomial Wigner-Ville distribution (FLOPWVD). The latter is able to reveal the instantaneous frequency of the high order polynomial phase signal (PPS) in the presence of impulsive noise modelled by an α-stable distribution. This new time-frequency distribution outperforms the standard PWVD, as is shown in simulation results.