The role of functional data analysis for instantaneous frequency estimation

This paper proposes a method for estimating the instantaneous frequency of a nonstationary signal; this method is based on a combination of empirical mode decomposition and functional data analysis. The proposed method incorporates a basis expansion technique for a functional data into time-varying phase derived by empirical mode decomposition and Hilbert transform, which provides a stable instantaneous frequency function. The superiority of the proposed method for instantaneous frequency estimation is demonstrated by various simulation studies. The analysis of multicomponent signals by the proposed method is also discussed. Furthermore, it is shown that the proposed method is highly effective for identifying groups (clusters) of nonstationary signals on the basis of the instantaneous frequency information.