Characterization of densities by moments
Leon W. Cohen · The Journal of the Acoustical Society of America · 1999
For two-dimensional classical densities it is very often the case that the general properties of a density can be characterized by low-order joint moments and conditional moments. The advantage of this is that moments and conditional moments are constants and one-dimensional functions, respectively, and hence can be more effectively used for characterization, classification, and detection than the full density. In the time-frequency case unique problems arise. First, the definition of conditional moments is problematic and has not been fully investigated. Second, since a time-frequency density may go negative the methods of probability theory may not be taken over directly. We investigate these issues and show that time-frequency conditional moments can be defined in such a way that they appropriately characterize the general features of a time-frequency density. [Work supported by ONR.]