**Lambert**. A project website for the course ELEC 301 at Rice University.

**EMD** (Empirical Mode Decomposition)
is an adaptive time-space analysis method suitable for processing series that
are non-stationary and non-linear. EMD performs operations that partition a
series into 'modes' (IMFs; Intrinsic Mode Functions) without leaving the
time domain. It can be compared to other time-space analysis methods like
Fourier Transforms and wavelet decomposition. Like these methods, EMD is
not based on physics. However, the modes may provide insight into various
signals contained within the data. In particular, the method is useful for
analyzing natural signals, which are most often non-linear and non-stationary.
Some common examples would include the Southern Oscillation Index (SOI), NINO-3.4 Index, etc.

**EEMD** (Ensemble EMD) is a *noise assisted* data analysis method.
EEMD consists of
*"sifting"* an ensemble of white noise-added signal.
EEMD can separate scales naturally without any a priori subjective criterion
selection as in the intermittence test for the original EMD algorithm.

Wu and Huang (2005) state: "White noise is necessary to force the ensemble to exhaust all possible solutions in the sifting process, thus making the different scale signals to collate in the proper intrinsic mode functions (IMF) dictated by the dyadic filter banks. As the EMD is a time space analysis method, the white noise is averaged out with sufficient number of trials; the only persistent part that survives the averaging process is the signal, which is then treated as the true and more physical meaningful answer." Further, they state: "[EEMD] represents a substantial improvement over the original EMD and is a truly noise assisted data analysis (NADA) method."

**CEEMDAN** (Complete Ensemble Empirical Mode Decomposition with Adaptive Noise)
is a variation of the EEMD algorithm that provides an exact reconstruction of the
original signal and a better spectral separation of the IMFs.

Some comments:

- Salisbury and Wimbush (2002):
"This empirical mode decomposition (EMD) method extracts the energy associated
with various intrinsic time scales in generating a collection of intrinsic mode
functions (IMFs). The IMFs have well-behaved Hilbert transforms, from which
instantaneous frequencies can be calculated. Thus, we can localize
any event in time as well as frequency."
- Lambert et al: "The fact that the functions into which a signal is decomposed are all in the time-domain and of the same length as the original signal allows for varying frequency in time to be preserved. Obtaining IMFs from real world signals is important because natural processes often have multiple causes, and each of these causes may happen at specific time intervals. This type of data is evident in an EMD analysis, but quite hidden in the Fourier domain or in wavelet coefficients."

**IMPORTANT NOTE:** NCL interfaces to C code
provided by Luukko et al. (2016). There have been reports that for
some of the modes, this code suffers from the mode mixing problem due
to the stoppage criterion that is used in P. Luukko's code. The NCL
team is looking into another version of EEMD to see if this issue can
be improved.