Robust wigner distribution with application to the instantaneous frequencyestimation

The Wigner distribution (WD) produces highly concentrated time-frequency (T F) representation of nonstationary signals. It may be used as an efficient signal analysis tool, including the cases of frequency modulated signals co rrupted with the Gaussian noise. In some applications, a significant amount of impulse noise is present. Then, the WD fails to produce satisfactory re sults. The robust periodogram has been recently introduced for spectral est imation of this kind of noisy signals. It can produce good concentration fo r pure harmonic signals. However, it is not so efficient in the cases of si gnals with rapidly varying frequency. This is the motivation for introducin g the robust WD. It is a reliable TF representation tool for wide class of nonstationary signals corrupted with impulse noise. This distribution produ ces good accuracy of the instantaneous frequency (IF) estimation. Using the Huber loss function, a generalization of the WD is presented. It includes both the standard and the robust WD as special cases. This distribution can be used for TF analysis of signals corrupted with a mixture of impulse and Gaussian noise. The presented theory is illustrated on examples, including applications on the IF estimation and time-varying filtering of signals co rrupted with a mixture of the Gaussian and impulse noise. The case study an alysis of the IF estimators' accuracy, based on the standard and the robust WD forms, is performed. In order to improve the IF estimation, a median fi lter is applied on the obtained IF estimate.