Multiple window spectrogram and time-frequency distributions

We extend the spectrum estimation method of Thomson (1982, 1990) to non-stationary signals by formulating a multiple window spectrogram. The traditional spectrogram can be represented as a member of Cohen´s class of time-frequency distributions (TFDs) where the smoothing kernel is the Wigner distribution of the signal temporal window. We show the unusual shape of the Cohen´s class smoothing kernels corresponding to the Thomson method multiple windows. These are a class of smoothing kernels not hitherto used in time-frequency (t-f) analysis. Examples of the multiple window spectrogram applied to a noisy dual linear FM test signal and to actual underwater acoustic data demonstrate the merit of the method