Empirical Mode Decomposition

Empirical mode decomposition is a data-driven method, which is a powerful tool for non-stationary signal analysis (Huang et al., 1998). This method decomposes a signal into slowly varying time dependent amplitudes and phases components named intrinsic mode functions. The time-frequency decomposition for the input signal is attributed to the Hilbert transform of the intrinsic mode functions extracted by the sifting process(Han and van der Baan, 2013). If $s(t)$ is the input signal, the empirical mode decomposition can be written as:

$$s(t) =\sum_{k=1}^{K} s_k (t)= \sum_{k=1}^{K} A_k (t)\cos (\phi_k(t)),$$ (1)

where $A_k(t)$ measures amplitude modulation, and $\phi_k(t)$ measures phase oscillation. Each $s_k(t)$ has a narrow-band waveform and an instantaneous frequency that is smooth and positive. The empirical mode decomposition is powerful, but its mathematical theory is sketchy.