Detection of Periodic Components from Intrinsic Mode Function

The empirical mode decomposition (EMD) combines with Hilbert Transform is a common method of nonlinear and non-stationary signal time frequency analysis. Signal can be decomposed into different intrinsic mode functions (IMF) through the EMD. Each IMF represents a simple oscillation which provides meaningful instantaneous frequency through Hilbert transform. The mode mixing of IMF is a critical problem which limits the performance of EMD. There are several reasons to cause mode mixing, the common reason is one IMF contains several periodic components. In order to solve this type of mode mixing, we propose an algorithm to detect and separate the periodic components from IMF. Each resulting periodic component can provide meaningful instantaneous frequency, and IMF can be replaced by the assemblage of all periodic components and the residuum. Our algorithm bases on the correlation coefficient between IMF slope segment and pure tone segment. The time resolution of this method depends on the duration of segment. We use three mode mixing examples to illustrate the good performance of our algorithm, includes the performance under additive white Gaussian noise.