Instrumentation & Measurement Magazine 23-2 - 55

Fig. 1. First round of sifting to extract IMF1. Its result is h1(t) [6].

Fig. 2. Second round of sifting to extract IMF1. Its result is h11(t) [6].

are met and remain the same [6]. Once S-number is selected,
IMF1 (c1(t)) can be obtained, as shown in (3). By repeating the
sifting process, the lower frequency component is repeatedly
removed from the highest frequency. So, c1(t) is the highest frequency, and it should represent the shortest period component
of the signal.
◗◗ The first IMF, (c1(t)), can be separated from the rest of the
data X(t), and the result is the first residue, r1(t), according to (4) [6].

shows r1(t) which is decomposed into c2(t) and r2(t) using sifting process.

	

r1 ( t ) = X ( t ) − c1 ( t )	(4)

The first residue, r1(t), is of lower frequency than the original signal, consists of several frequencies and contains longer
period variations in the data. X(t), IMF1 (c1(t)), and r1(t) are
shown graphically in Fig. 3. r1(t) is treated as the new data and
subjected to the same sifting process to obtain the second IMF
component (IMF2), c2(t), and second residue, r2(t), as described
in the steps above. The difference between r1(t) and c2(t) is r2(t)
which is of lower frequency than r1(t), as shown in (5). Fig. 4

	

r2 ( t ) = r1 ( t ) − c2 ( t )	(5)

By repeating sifting, the number of extrema will be reduced as the procedure continues. So, a signal is sequentially
decomposed into a finite number (n) of IMFs, where the highest frequency component is represented by IMF1 ( t ) and the
lowest frequency component is represented by IMFn ( t ) and
a residue rn(t). Finally, the original signal X(t) can be decomposed into n IMFs and rn, using the sifting process of EMD,
as shown in (6) [6]. This means that the sifting process will finally stop when the residue becomes a monotonic function
from which no more IMFs can be extracted. Fig. 5 shows a
complete decomposition example where the original signal
X(t) is decomposed into IMF1(t), IMF2(t), IMF3(t) and a monotonic function r3(t).
n

	

X ( t ) = IMFi ( t ) + rn ( t )	(6)
i =1

April 2020	

IEEE Instrumentation & Measurement Magazine	55



Instrumentation & Measurement Magazine 23-2

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