The term [[phi].sub.j](t) is the

instantaneous phase of x (t).

In order to perform PS analysis,

instantaneous phase information of EEG signals must be extracted.

Then, the

instantaneous phase [[empty set].sub.1](t) of [x.sub.1](t) was defined as

If is the time delay between the transmitted and received signal of the same target is [tau], then the

instantaneous phase of received signal is

By performing Hilbert transform on the known earthquake record, the instantaneous amplitude and the

instantaneous phase of the earthquake record can be obtained.

The instantaneous amplitude is the amplitude of the complex HT (analytical signal) and the instantaneous frequency is the rate of change of the

instantaneous phase angle (see (4)).

The Kuramoto parameter measures the

instantaneous phase angle of several signals.

The instantaneous frequency is defined as the derivative of the

instantaneous phase:

After the data has been decomposed into IMFs, the second step is to apply the Hilbert transform to each IMF, which produces

instantaneous phase (frequencies) as functions of time.

Instantaneous phase and instantaneous frequency can be determined by (Eq.

where [P.sub.0] is the constant average power of the laser and [[theta].sub.E](t) is the

instantaneous phase of the signal E(t).

Features used in this paper are Standard deviation of absolute value of the centered non-linear components of

instantaneous phase ( ) Standard deviation of direct value of the centered non-linear components of

instantaneous phase ( Standard deviation of absolute value of the normalized centered instantaneous amplitude (