Instantaneous frequency estimation of FM signals by ΨB-energy operator

The Ψ_B energy operator is an extension of the cross-Teager-Kaiser energy operator which is a nonlinear energy tracking operator to deal with complex signals and its usefulness for non-stationary signals analysis has been demonstrated. Two new properties of Ψ_B are established. The first property is the link between Ψ_B and the dynamic signal which is a generalisation of the instantaneous frequency (IF). The second property obtained for frequency modulated (FM) signals is a simple way to estimate the IF. These properties confirm the interest of the Ψ_B operator to track the non-stationarity of a signal. Results of IF estimation in a noisy environment of a nonlinear FM signal are presented and comparison to the Wigner-Ville distribution and the Hilbert transform-based method is provided.