Eliminating interference terms in the Wigner distribution using extended libraries of bases

The Wigner distribution (WD) possesses a number of desirable mathematical properties relevant to time-frequency analysis. However, the presence of interference terms renders the WD of multicomponent signals extremely difficult to interpret. We propose an adaptive decomposition of the WD using extended libraries of orthonormal bases. A prescribed signal is expanded on a basis of adapted waveforms, that best match the signal components, and subsequently transformed into the Wigner domain. The interference terms are controlled by thresholding the cross WD of interactive basis functions according to their degree of adjacency in an idealized time-frequency plane. This measure is implicitly adapted to the local distribution of the signal, thus compensating for a global nonadaptive threshold. In particular we focus on a shift-invariant decomposition in an extended library of wavelet packets. The resulting modified distribution achieves high time-frequency resolution, and is superior in eliminating interference terms associated with bilinear distributions