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 is the input signal, the empirical mode decomposition can be written as:
where measures amplitude modulation, and measures
phase oscillation. Each 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.