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.
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 (