Improved EMD for the analysis of FM signals
In this paper, an innovative algorithm of improved EMD (IEMD) has been presented for the analysis of frequency modulation (FM) signals. First, extract the first level extrema and the second level extrema to construct one two-level extrema structure (TLES). Using the locations' relations between the first level extrema and the second level extrema, what the traditional EMD does for FM signals is determined. The propositions that can help us to judge whether the multi-component can be separated well or not by EMD in practice and then tell us what the EMD will do in practice are deduced. Four cases are presented for decomposition of FM components using EMD. According to these cases, different improved methods are presented to separate the FM components that EMD fails to separate. The least-squares method is used to estimate the phase polynomials of FM components. The orthogonal relations between different components are used to estimate the optimal amplitudes of FM components. Moreover, the performance of EMD is analyzed via the multi-level extrema distribution as well, which can be used in practice for the aforehand judgement. Finally, experiments are given to show our new improved EMD.
frequency modulation (fm) two-level extrema structure (tles) least-squares method empirical mode decomposition (emd) tf distribution mono-component and multi-component