Multiple window spectrogram and time-frequency distributions

We extend the spectrum estimation method of Thomson 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 mnltiple window spectrogram applied to a noisy dual linear FM test signal and t o actual underwater acoustic da ta demonstrate the merit of the method.