Time-varying spectrum estimators

The quadratic time-frequency representations (TFRs) that may be called time-varying spectrum estimators are derived from first principles. They turn out to be time-varying multiwindow spectrum estimators. In special cases they are time-varying spectrograms that may be written as Fourier transforms of lag-windowed, time-varying correlation sequences or as spectrally smoothed time-varying periodograms. These are not ad-hoc variations on stationary ideas to accommodate time variation. Rather they are the only variations one can obtain for time-varying spectrum analysis.