Component enumeration of multicomponent AM-FM signals via generalized energy operators

Enumerating the number of signal components present in a superposition of signals is a problem that finds application in radar systems, multiuser communication problems, beamforming and array processing applications. The related problem of enumerating the number of components present in a superposition of non-stationary signals is a more challenging problem because of the nature of the components that may be well separated in frequency at one instant and overlap at a later instant. In this paper, we apply the Teager-Kaiser energy operator and higher-order generalizations of the operator to the problem of non-stationary signal component enumeration. The singularity of these instantaneous signal operators is used as a cue to track the number of components present in a multicomponent AM-FM signal.