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

摘要

Using the orthogonal-like Gabor expansion, the authors decompose the Wigner-Ville distribution (WVD) to a linear combination of localized and symmetric functions WVD/sub h, h'/ (t, w), the WVD of the Gabor elementary functions, h/sub m, n/(t) and h/sub m'n'/(t). Since the influence of the WVD/sub h, h'/(t, w) to the useful properties is inversely proportional to the distance between h/sub m, n/ (t) and h/sub m', n't/, the WVD/sub h, h'/(t, w) are further grouped as a series of the function P/sub 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/sub d/(t, w). While TFDS/sub 0/(t, w)=P/sub 0/(t, w) is similar to the spectrogram, TFDS/sub /spl infin//(t, w) converges to the WVD/sub 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.