Hankel and Toeplitz kernels for time-varying spectrum estimation

Some quadratic time-frequency representations (TFRs) may be called time-varying spectrum estimators. When the kernel of the TFR is factored as a diagonal-Toeplitz-diagonal operator then the TFR is a time-varying spectrogram that may be written any one of three ways: as a Fourier transform of a lag-windowed time-varying correlation sequence, as a spectrally-smoothed time-varying periodogram, or as a multiple-window spectrogram. If the kernel of the TFR is factored as a diagonal-Hankel-diagonal operator then the TFR is a generalized Wigner-Ville distribution.