Spectral decomposition of time-frequency distribution kernels

It is shown that the singular-value decomposition (SVD) of the time-frequency kernels allows the expression of the time-frequency distributions in terms of weighted sum of smoothed pseudo Wigner-Ville distributions or modified periodograms, which are the two basic nonparametric power distributions for stationary and nonstationary signals, respectively. The windows appearing in the decomposition take zero and/or negative values and, therefore, are different from the time and lag windows commonly employed by these two distributions. The decomposition windows can be data-dependent or fixed, depending on whether the interest is to approximate the time-frequency distribution for a given data record, or for a Gaussian stationary white noise process