The author summarizes the development of a data-adaptive smoothed Wigner-Ville function (WVF) time-frequency representation (TFR) that suppresses cross terms and noise effects. A Gabor TFR of a data set is performed to obtain the Gabor coefficients relative to the selected Gabor basis wavelet. Because the Gabor TFR involves only linear operations on the data, no cross-term artifacts are introduced. Published maximum likelihood tests can then be applied to the Gabor coefficients to sort those estimated to be signal-related Gabor coefficients from those estimated to be noise-related coefficients (Friedlander and Porat, 1987, 1989, 1992). The signal-related Gabor coefficients only are then used to form a data-adaptive multiplicative weighting kernel applied to the complex ambiguity function computed from the data which is double Fourier transformed to create a filtered WVF TFR. This processing approach retains the usual time-frequency localization properties of the WVF on actual signal components, while suppressing the effect of cross terms and noise components by essentially forcing the WVF TFR to have zero support where zero support was found in the Gabor TFR.
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