A novel technique to reduce cross terms in the squared magnitude of the wavelet transform and the short-time Fourier transform

The energy distribution of a non-stationary signal is often represented by the squared magnitude of the wavelet transform (WT) or the short-time Fourier transform (STFT). The energy distribution contains cross terms which can cause problems while analyzing the multicomponent signals. In this paper, a unified approach is developed for the time-frequency analysis of a multicomponent signal without introducing cross terms. The Fourier-Bessel (FB) series expansion of the multicomponent signal is used for separating and reconstructing the individual components of the signal, and then, the time-frequency energy distributions are computed for the individual components. The simulation results show that the proposed approach based on the FB series expansion is a powerful tool for analyzing multicomponent signals.