ABSTRACT
Signal can be decomposed into a set of intrinsic mode functions (IMFs) by the empirical mode decomposition (EMD) which is also called Huang Transform. EMD is a process of cyclic decomposition. The complete decomposition process can be found in
literature (Cheng 2006). Using EMD method, the original data s(t) can be expressed as a sum of the IMFs and a residue:
s t c t r t( ) ( ) ( )i n i
1 ∑= +
(1)
For an time series x(t), its Hilbert transform y(t) can be presented as
y t p x t t t
dt( ) 1 ( )∫pi= ′− ′ ′ (2)
Each IMF of s(t) is applied the Hilbert transform, then H t( , )ω , the time-frequency spectrum, can be obtained and written as (Cheng 2009):
H t a t e( , ) Re ( )j i dt
j∑ω = ∫ω =
(3)
The function H(ω,t) is defined as Hilbert spectrum to reveal time-frequency distribution of original signal. Then, the Hilbert marginal spectrum is presented as:
h H t dt( ) ( , ) T
0∫ω ω= (4) T is the length of time series.
