Enhanced Time–Frequency Representation Based on Variational Mode Decomposition and Wigner–Ville Distribution

Abstract

The Wigner–Ville distribution (WVD) gives a very high-resolution time–frequency distribution but diminishes due to the existence of cross-terms. The cross-terms suppression in WVD is crucial to get the actual energy distribution in time–frequency (TF) plane. This chapter proposes a method to remove both inter and intra cross-terms from TF distribution obtained using WVD. The variational mode decomposition is applied to decompose a multicomponent signal into corresponding mono-components and inter cross-terms are suppressed due to the separation of mono-components. Thereafter, segmentation is applied in time domain to remove intra cross-terms present due to nonlinearity in frequency modulation. The obtained components are processed to get WVD of each component. Finally, all the collected WVDs are added to get complete time–frequency representation. Efficacy of the proposed method is checked using Renyi entropy measure over one synthetic and two natural signals (bat echo sound and speech signal) in clean and noisy environment. The method presented works well and gives better results in comparison to the WVD and pseudo WVD techniques.