Adaptive time-frequency distributions via the shift-invariant wavelet packet decomposition

Utilizing the shift-invariant wavelet packet decomposition (SIWPD), various useful properties relevant to time-frequency analysis, including high energy concentration and suppressed interference terms, can be achieved simultaneously in the Wigner domain. A prescribed signal is expanded on its best basis and transformed into the Wigner domain. Subsequently, the interference terms are eliminated by adaptively thresholding the cross Wigner distribution of interactive basis functions, according to their amplitudes and distance in an idealized time-frequency plane. The properties of the resultant modified Wigner distribution (MWD) are investigated, and its performance in eliminating interference terms, while still retaining high energy resolution, is compared with that of other existing approaches. We demonstrate the effectiveness of the proposed MWD to resolving multicomponent signals. Each component is determined as a partial sum of basis-functions over a certain equivalence class in the time-frequency plane.