*4.2. Empirical Mode Decomposition*

In contrast to other decomposition methods, empirical mode decomposition (EMD) does not entail predetermining a basis function. In EMD, such a function is directly obtained from the signal data; therefore, this method has considerable flexibility. EMD entails decomposing an original signal

into a finite number of intrinsic mode function (IMF) components; specifically, a signal is approximated as a sum of zero-mean amplitude modulation and frequency modulation components. The finite number of IMF components can be divided into high- and low-frequency partitions until a monotonic function (trend) remains. The original data can be regarded as the sum of all IMF components and trends. During analysis, if the time difference between the extreme values represents the time scalar of the intrawave, an optimal vibration modal resolution can be achieved and can be applied to nonzero mean values as well as non-zero-crossing data. Thus, the original signal can be re-presented as

$$X(t) = \sum\_{i=1}^{n} c\_i + r\_n \tag{15}$$

where *Ci* is the *i*th intrinsic mode functions; *rn* is the residual.
