A method to eliminate riding waves appearing in the empirical AM/FM demodulation

Empirical mode decomposition can decompose a complicated signal into a sum of finite intrinsic mode functions whose instantaneous frequencies computed by the analytic signal method give a physically meaningful characterization of the signal. However, it is found that computing the instantaneous frequency of an intrinsic mode function through the Hilbert transform may produce some ridiculous results. Recently, an empirical AM/FM (amplitude and frequency modulation) demodulation for computing the instantaneous frequency of an intrinsic mode function has been proposed by Huang and his coworkers. This method totally eschews the Hilbert transform and can compute the instantaneous frequency of an intrinsic mode function very accurately. However, this paper will show that the empirical FM part extracted through the empirical AM/FM demodulation may contain riding waves and is no longer an intrinsic mode function. That will make the instantaneous frequency nonsensical. To overcome this drawback, an improved method, called riding wave turnover-empirical AM/FM demodulation, is proposed in this paper. Experiments show very positive results.