Definitions of Instantaneous Frequency under physical constraints

Villeʹs definition of Instantaneous Frequency (IF), even though widely used and accepted, fails in most cases of practical interest. This failure has been often reported, namely in the multicomponent case. In this paper, we will analyze the advantages and shortcomings of that definition, and determine when and why it fails, integrating all previously reported cases of failure in a simple unified theory. We will also be able to extrapolate and predict the behavior of the traditional definition for any type of multicomponent signal. Alternative definitions of IF are discussed.