Classification of Normal and Epileptic Seizure EEG Signals Based on Empirical Mode Decomposition - Complex System Modelling and Control Through Intelligent Soft Computations - page 366

2.2 Empirical Mode Decomposition

The main idea of empirical mode decomposition (EMD) is based on the assumption
that any signal comprises of different simple mode of oscillations (Huang et al. 1998 ).
It is a data dependant signal processing technique that represents any temporal signal
into a finite set of amplitude and frequency modulated (AM-FM) oscillating com-

ponents termed as intrinsic mode functions (IMFs). It is noteworthy that this method
of decomposition does not require any prior assumption about the stationarity and
linearity of signal. The EMDmethod decomposes a complicated signal x(t) iteratively
into a set of the band-limited IMFs, I m ð t Þ ;

where m ¼ 1 2

; ... ; M (Huang et al. 1998 ).

;

Each of these IMFs satis es the following two basic conditions:

1. The number of extrema and the number of zero crossings must be either equal or
differ at most by one,
2. The mean value of the envelopes de ned by the local maxima and that of

de ned by the local minima must be zero.

The EMD algorithm to extract IMFs from a signal x ð t Þ can be explained in fol-

lowing steps (Huang et al. 1998 ):

1. Find all the local maxima and local minima in the signal x .

2. Connect all the maxima and all the minima separately in order to get the
envelopes E max ð

ð t Þ

respectively.
3. Compute the mean value of the envelopes by using the following formula:

t Þ and E min ð t Þ

E max ð t Þþ E min ð t Þ

m ð t Þ ¼ ð 1 Þ

2

4. Subtract m ð t Þ from signal x ð t Þ as:

g 1 ð t Þ ¼ x ð t Þ m ð t Þ ð 2 Þ

5. Check if the g 1 ð t Þ satis es the conditions for IMF as mentioned above or not.

6. Repeat the steps 2 5 until IMF is obtained.

-

After obtaining rst IMF de ne I 1 ð t Þ ¼ g 1 ð t Þ which is smallest temporal scale in x ð t Þ .

Next IMF can be derived by generating a residue r 1 ð which can be

used as the new signal for above algorithm. The process is repeated until the residue
obtained becomes a constant or monotonic function from which no more IMF can be
generated. The obtained IMFs are a set of narrow-band symmetric waveforms. After
the decomposition, the signal x

t Þ ¼ x ð t Þ I 1 ð t Þ

ð t Þ can be represented as follows (Huang et al. 1998 ):

X

M

x ð t Þ ¼ I m ð t Þþ r M ð t Þ ð 3 Þ

m ¼ 1

where, M is the number of IMFs, I m ð t Þ is the mth IMF and r M ð t Þ is the final residue.