DECOMPOSITION OF THE WIGNER-VILLE DISTRIBUTION AND TIME-FREQUENCY DISTRIBUTION SERIES

Using the orthogonal like Gabor expansion, we decompose the Wigner-Vil le distribution (WVD) to a linear combination of localized and symmetr ic functions WVDh,h'(t,w), the WVD of the Gabor elementary functions, h(m,n)(t) and h(m',n')(t). Since the influence of the WVDh,h'(t,w) to the useful properties(1) is inversely proportional to the distance bet ween h(m,n)(t) and h(m',n')(t), the WVDh,h'(t,w) are further grouped a s a series of the function Pd(t,w). We name the resulting representati on the time-frequency distribution series (TFDS) (also know n as the G abor Spectrogram in industry). The TFDSD consists of up to a Dth order P-d(t,w). While TFDSo(t,w) = P-o(t,w) is similar to the spectrogram, TFDSinfinity(t,w) converges to the WVDs(t,w). Numerical simulations de monstrate that adjusting the order D of the TFDS, one could effectivel y balance the cross-term interference and the useful properties.