Robust time-frequency representations for signals in α-stable noise using fractional lower-order statistics

Characterizing signals jointly in the time and frequency domains through time-frequency representations (TFRs) such as the Wigner-Ville distribution (WVD) is a natural extension of Fourier analysis and gives a more complete representation of signal behavior particularly in the case of non-stationary signals. In the presence of additive impulsive noise, TFRs quickly break down and any information about the desired signal is lost. To combat these effects, we propose in this paper a family of memoryless nonlinearities which have been shown to produce a signal autocorrelation statistic which is well-behaved in the presence of stable noise. The result of this approach is a TFR which is both robust and simple to implement, and has many of the mathematical properties associated with the standard WVD. We illustrate the improvement in performance that can be obtained with several examples