Decomposition of the Wigner-Ville distribution and time-frequency distribution series

Using the orthogonal-like Gabor expansion, the authors decompose the Wigner-Ville distribution (WVD) to a linear combination of localized and symmetric functions WVD_{h, h´} (t, w), the WVD of the Gabor elementary functions, h_{m, n}(t) and h_m´n´(t). Since the influence of the WVD_{h, h´}(t, w) to the useful properties is inversely proportional to the distance between h_{m, n} (t) and h_{m´, n´t}, the WVD_{h, h´}(t, w) are further grouped as a series of the function P_d(t, w). The authors name the resulting representation the time-frequency distribution series (TPDS) (also known as the Gabor spectrogram in industry). The TFDSD consists of up to a Dth order P_d(t, w). While TFDS₀(t, w)=P₀(t, w) is similar to the spectrogram, TFDS_∞(t, w) converges to the WVD_s (t, w). Numerical simulations demonstrate that adjusting the order D of the TFDS, one could effectively balance the cross-term interference and the useful properties