Optimal multiple window time-frequency analysis of locally stationary processes

This paper investigates the multiple windows of the mean squared error optimal time-frequency kernel for estimation of the Wigner-Ville spectrum. The kernel is optimal for a certain locally stationary process where the covariance function is determined by two one-dimensional Gaussian functions. The multiple windows are obtained as the eigenvectors of the rotated time-lag estimation kernel. The spectrograms from the different windows are weighted with the eigenvalues and the resulting multiple window spectrogram is an estimate of the optimal smoothed Wigner-Ville spectrum.