A window based method to reduce the end-effect in empirical mode decomposition

Empirical Mode Decomposition technique (EMD) is a recent development in non-stationary and non-linear data analysis. It is an algorithm that adaptively decomposes the signal in the sum of Intrinsic Mode Functions (IMFs) from which the instantaneous frequency can be easily computed. Differently from the Fourier Transform, the EMD does not decompose a signal into stationary harmonic components, but into a finite and small number of IMFs based on the local characteristic time scale of the data. EMD has been widely applied in different fields as seismic studies, structural health monitoring, whether forecast, image processing and financial applications. More recently different authors proposed the use of EMD for condition monitoring purpose, e.g. in bearing or gear diagnostics. EMD has proven its effectiveness, but is still affected from various computational problems. One of these is the “end-effect”, a phenomenon occurring at the beginning and at the end of the data due to the splines fitting on which the EMD is based. Different spline fitting introduces different instantaneous frequency components that may unnecessarily complicate the data analysis. Various techniques have been tried to overcome the end-effect, like different data extension or mirroring procedures at the data boundary. This paper proposes a windowing process to manage the end-effect phenomenon. Recently other researchers have covered the windowing approach, suggesting classic windows like Hanning or flat-top, but results are highly dependent of the processed data. In this paper it has made use of the IMFs orthogonality property to apply a symmetrical polynomial window to the data before EMD for end-effect reduction. Subsequently the IMFs are post-processed to compensate for data alteration due to windowing. The procedure is applied to simulated data to easily take into account different kind of sources like trend, chirp, etc. The simulations show that IMFs obtained with this method may prove a reduced end-effect, while they are almost identical to classical EMD ones in other cases, depending on the data complexity.