Hilbert transform is one of the methods to describe signal analysis and complex envelope in the field of mathematics and signal processing and it can be roughly described as the convolution of a signal s(t) with 1/[pi]t to get the signal s'(t) [8].

Then he further put forward the Hilbert-Huang transform (HHT) combined with

Hilbert transform. The analyzed signal was decomposed into several intrinsic mode functions (IMF).

Next, apply the

Hilbert transform to all IMFs, to derive model parameters including frequency and damping:

Each IMF obtained by using

Hilbert transform time is put forward for frequency analysis [35].

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.

In addition, the generalized

Hilbert transform closely related to SAFT, called offset

Hilbert transform (OHT), is another powerful tool in the fields of optics and signal processing community [15].

Hilbert Transform. The

Hilbert transform (HT) is defined by the real-valued folding operation on the realvalued signal s(t)

In this study, we systematically used the

Hilbert Transform (HT) approach to compute the PRC from experimental data and showed that the results are independent of the arbitrary and often problematic definition of phase reference.

proposed Hilbert-Huang transform (HHT) method, which is a new, self-adaptive frequency analysis method [9], and included the empirical mode decomposition (EMD) and

Hilbert transform (HT); the core is the EMD.

To apply the proposed method in practical application (directed acoustic transmission-reception system in our case), it is necessary to obtain the echo shape derived from experiments, so

Hilbert transform is used to extract the received signal envelop, and the extracted envelop is used to modulate the transmitted signal.

In the present paper, a simplified conditional simulation method of synthesizing spatially correlated earthquake ground motions is proposed based on

Hilbert transform and earthquake record.

For any real IMF c(t), its

Hilbert transform cH(t) is defined as