Spectrogram decompositions of time-frequency distributions

This paper outlines means of combining spectrograms formed using specially designed windows. Previous work has shown that one can decompose any time-frequency distribution (TFD) in Cohen's class into a weighted sum of spectrograms. This is accomplished by decomposing the kernel of the distribution in terms of an orthogonal set of analysis windows. The spectrograms obtained using these analysis windows are then linearly combined with proper weights to form the desired TFD. The goal is a full and effective basis for representing TFD. Successful application of this theory offers very fast computation of TFD, since very few analysis windows may be needed and fast, recursive spectrogram algorithms can be used.