Optimum window time-frequency distribution decompositions

This paper introduces a new approach for decomposing time-frequency distributions in terms of weighted series of spectrograms. 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 TFDS. Successful application of this theory offers very fast computation of TFDs, since very few "wavelet-like" analysis windows may be needed and fast, recursive spectrogram algorithms can be used. Finally, a minimum window Reduced interference Distribution (M-RID) is introduced.