Instantaneous frequency of mono and multicomponent signals

It has often been reported and is now well established that the traditional definition of instantaneous frequency (IF_t) fails in the presence of multicomponent signals. New definitions of IF_t have been proposed, in an attempt to cope with the difficulties of the traditional one. We address the reasons for failure of the traditional definition, show that it can also fail with monocomponent signals, and show how its behaviour can be predicted for any type of signal, thus generalizing previous results. We also analyse the performance in noise of one of the previously proposed definitions of IF _t