The complex local mean decomposition

Keywords: Local mean decomposition Data fusion Complex signal analysis Time–frequency analysis Signal nonlinearity Spike identification a b s t r a c t The local mean decomposition (LMD) has been recently developed for the analysis of time series which have nonlinearity and nonstationarity. The smoothed local mean of the LMD surpasses the cubic spline method used by the empirical mode decomposition (EMD) to extract amplitude and frequency modulated components. To process complex-valued data, we propose complex LMD, a natural and generic extension to the complex domain of the original LMD algorithm. It is shown that complex LMD extracts the frequency modulated rotation and envelope components. Simulations on both artificial and real-world complex-valued signals support the analysis. Standard signal analysis techniques, such as Fourier analysis, are based on assumptions of linearity and stationarity of the signal. Since most real-world signals contain nonlinearity 1 and nonstationarity, 2 time–frequency analysis techniques such as the short time Fourier transform (STFT) and the wavelet transform (WT) have attracted considerable attention. However, their application is often limited since they are based on a projection onto a predefined set of basis functions [3]. Recent research on signal decomposition has been based on fully data-driven techniques, exploratory data analysis (EDA) [4]. One such technique is empirical mode decomposition (EMD), which is a fully adaptive approach that decomposes the signal into a finite set of AM/FM components [5]. EMD makes no prior assumptions on the data and, as such, it is ideal for the analysis of nonlinear and nonstationary data. Due to the monocomponent nature of its decomposition, the Hilbert transform can be applied to obtain an analytic representation for the signal, from which the instantaneous frequency (IF) and instantaneous amplitude (IA) can be determined. EMD has found numerous applications, including radar technology [6] and biomedical engineering [7–9]. However, the use of cubic splines and the Hilbert transform in the EMD process induces a loss of amplitude and frequency information [10], as illustrated by an often erratic or negative IF. To this end, the local mean decomposition (LMD) was recently introduced [10]. LMD uses smoothed local means to determine a more credible and reliable IF directly from the oscillations within the signal without the Hilbert transform. Its application has been originally illustrated on electro-encephalogram (EEG) [10], and in [11,12] it was shown how LMD facilitated enhanced analysis compared to EMD in rub-impact fault diagnosis. Real-valued data sources, for which …