On the instantaneous frequencies of multicomponent AM-FM signals

We study the instantaneous frequencies (IFs) of multicomponent AM-FM signals by extending the work on the two-component case by Loughlin and Tacer (see ibid.,, vol. 4, no.5, p.123-25, 1997) to the more general M-component case. A novel necessary and sufficient condition for the valid interpretation of the IF as a nonnegatively weighted average of the IFs of the components is proposed, which we apply as a method of interpreting the IFs of signals having no more than three dominant components at each time. Our quantitative study shows that in general, the IF-based monocomponent AM-FM decomposition is not appropriate for the modeling and analysis of multicomponent AM-FM signals unless all the components are well separated in the time domain.