Modeling and Denoising Wigner-Ville Distribution

Abstract

Due to the bilinear nature of Wigner-Ville and other time-frequency distributions, they produce poor results in the presence of additive noise. Though smoothed versions of the Wigner-Ville distribution (WVD) such as smoothed pseudo Wigner-Ville distribution (SPWVD) can suppress the noise effect, they still contain considerable noise. In this paper, we introduce a novel noise suppression method for WVD and its smoothed version, SPWVD, based on non-linear, non-Gaussian modeling of these distributions. We demonstrate that these distributions have significantly non-Gaussian statistics that are appropriately described by two-dimensional Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model. Then, we apply a maximum a-posteriori (MAP) estimator for estimating the clean distributions based on GARCH modeling. Furthermore, we apply denoised distributions for estimating the instantaneous frequency (IF) of signals such as radar's Doppler frequency. Experimental results demonstrate the efficiency of proposed method in denoising WVD and SPWVD and also in IF estimation.