Intrinsic Fourier Mode Functions

Abstract

In this paper, we study a class of functions that exhibit properties expected from intrinsic mode functions. A type of an empirical instantaneous frequency, depending on the extrema scale, is introduced and its proximity to the classical analytic instantaneous frequency is discussed. We also obtain a sufficient condition for positiveness of the instantaneous frequency and introduce a method similar in nature to EMD but with an empirical frequency as guide in lieu of empirical envelopes. The method is illustrated in several numerical examples.