<s>
The	O
Hilbert	B-Algorithm
–	I-Algorithm
Huang	I-Algorithm
transform	I-Algorithm
(	O
HHT	O
)	O
is	O
a	O
way	O
to	O
decompose	O
a	O
signal	O
into	O
so-called	O
intrinsic	O
mode	O
functions	O
(	O
IMF	O
)	O
along	O
with	O
a	O
trend	O
,	O
and	O
obtain	O
instantaneous	O
frequency	O
data	O
.	O
</s>
<s>
It	O
is	O
designed	O
to	O
work	O
well	O
for	O
data	O
that	O
is	O
nonstationary	B-Algorithm
and	O
nonlinear	O
.	O
</s>
<s>
In	O
contrast	O
to	O
other	O
common	O
transforms	O
like	O
the	O
Fourier	B-Algorithm
transform	I-Algorithm
,	O
the	O
HHT	O
is	O
an	O
algorithm	O
that	O
can	O
be	O
applied	O
to	O
a	O
data	O
set	O
,	O
rather	O
than	O
a	O
theoretical	O
tool	O
.	O
</s>
<s>
The	O
Hilbert	B-Algorithm
–	I-Algorithm
Huang	I-Algorithm
transform	I-Algorithm
(	O
HHT	O
)	O
,	O
a	O
NASA	O
designated	O
name	O
,	O
was	O
proposed	O
by	O
Norden	O
E	O
.	O
Huang	O
et	O
al	O
.	O
</s>
<s>
It	O
is	O
the	O
result	O
of	O
the	O
empirical	O
mode	O
decomposition	O
(	O
EMD	O
)	O
and	O
the	O
Hilbert	B-Algorithm
spectral	I-Algorithm
analysis	I-Algorithm
(	O
HSA	O
)	O
.	O
</s>
<s>
The	O
HHT	O
provides	O
a	O
new	O
method	O
of	O
analyzing	O
nonstationary	B-Algorithm
and	O
nonlinear	O
time	O
series	O
data	O
.	O
</s>
<s>
Breaking	O
down	O
signals	O
into	O
various	O
components	O
,	O
EMD	O
can	O
be	O
compared	O
with	O
other	O
analysis	O
methods	O
such	O
as	O
Fourier	B-Algorithm
transform	I-Algorithm
and	O
Wavelet	B-Algorithm
transform	I-Algorithm
.	O
</s>
<s>
Without	O
leaving	O
the	O
time	O
domain	O
,	O
EMD	O
is	O
adaptive	B-Algorithm
and	O
highly	O
efficient	O
.	O
</s>
<s>
Since	O
the	O
decomposition	O
is	O
based	O
on	O
the	O
local	O
characteristic	O
time	O
scale	O
of	O
the	O
data	O
,	O
it	O
can	O
be	O
applied	O
to	O
nonlinear	O
and	O
nonstationary	B-Algorithm
processes	O
.	O
</s>
<s>
It	O
represents	O
a	O
generally	O
simple	O
oscillatory	B-Algorithm
mode	O
as	O
a	O
counterpart	O
to	O
the	O
simple	O
harmonic	O
function	O
.	O
</s>
<s>
This	O
definition	O
guarantees	O
a	O
well-behaved	O
Hilbert	B-Algorithm
transform	I-Algorithm
of	O
the	O
IMF	O
.	O
</s>
<s>
Hilbert	B-Algorithm
spectral	I-Algorithm
analysis	I-Algorithm
(	O
HSA	O
)	O
is	O
a	O
method	O
for	O
examining	O
each	O
IMF	O
's	O
instantaneous	O
frequency	O
as	O
functions	O
of	O
time	O
.	O
</s>
<s>
The	O
final	O
result	O
is	O
a	O
frequency-time	O
distribution	O
of	O
signal	O
amplitude	O
(	O
or	O
energy	O
)	O
,	O
designated	O
as	O
the	B-Algorithm
Hilbert	I-Algorithm
spectrum	I-Algorithm
,	O
which	O
permits	O
the	O
identification	O
of	O
localized	O
features	O
.	O
</s>
<s>
The	O
empirical	O
mode	O
decomposition	O
(	O
EMD	O
)	O
method	O
is	O
a	O
necessary	O
step	O
to	O
reduce	O
any	O
given	O
data	O
into	O
a	O
collection	O
of	O
intrinsic	O
mode	O
functions	O
(	O
IMF	O
)	O
to	O
which	O
the	O
Hilbert	B-Algorithm
spectral	I-Algorithm
analysis	I-Algorithm
can	O
be	O
applied	O
.	O
</s>
<s>
IMF	O
represents	O
a	O
simple	O
oscillatory	B-Algorithm
mode	O
as	O
a	O
counterpart	O
to	O
the	O
simple	O
harmonic	O
function	O
,	O
but	O
it	O
is	O
much	O
more	O
general	O
:	O
instead	O
of	O
constant	O
amplitude	O
and	O
frequency	O
in	O
a	O
simple	O
harmonic	O
component	O
,	O
an	O
IMF	O
can	O
have	O
variable	O
amplitude	O
and	O
frequency	O
along	O
the	O
time	O
axis	O
.	O
</s>
<s>
Connect	O
all	O
the	O
local	O
maxima	O
by	O
a	O
cubic	B-Algorithm
spline	I-Algorithm
line	I-Algorithm
as	O
the	O
upper	O
envelope	O
.	O
</s>
<s>
Having	O
obtained	O
the	O
intrinsic	O
mode	O
function	O
components	O
,	O
the	O
instantaneous	O
frequency	O
can	O
be	O
computed	O
using	O
the	O
Hilbert	B-Algorithm
transform	I-Algorithm
.	O
</s>
<s>
After	O
performing	O
the	O
Hilbert	B-Algorithm
transform	I-Algorithm
on	O
each	O
IMF	O
component	O
,	O
the	O
original	O
data	O
can	O
be	O
expressed	O
as	O
the	O
real	O
part	O
,	O
Real	O
,	O
in	O
the	O
following	O
form	O
:	O
</s>
<s>
 [ 2003b ] 	O
applied	O
HHT	O
to	O
nonstationary	B-Algorithm
financial	O
time	O
series	O
and	O
used	O
a	O
weekly	O
mortgage	O
rate	O
data	O
.	O
</s>
<s>
A	O
source	O
code	O
to	O
realize	O
the	O
arbitrary	O
order	O
Hilbert	B-Algorithm
spectral	I-Algorithm
analysis	I-Algorithm
can	O
be	O
found	O
at	O
.	O
</s>
<s>
Meteorological	O
and	O
atmospheric	O
applications	O
:	O
Salisbury	O
and	O
Wimbush	O
[2002],	O
using	O
Southern	O
Oscillation	B-Algorithm
Index	O
data	O
,	O
applied	O
the	O
HHT	O
technique	O
to	O
determine	O
whether	O
the	O
Sphere	O
of	O
influence	O
data	O
are	O
sufficiently	O
noise	O
free	O
that	O
useful	O
predictions	O
can	O
be	O
made	O
and	O
whether	O
future	O
El	O
Nino	O
southern	O
oscillation	B-Algorithm
events	O
can	O
be	O
predicted	O
from	O
SOI	O
data	O
.	O
</s>
<s>
 [ 2002 ] 	O
used	O
HHT	O
to	O
analyze	O
satellite	B-Application
scatterometer	O
wind	O
data	O
over	O
the	O
northwestern	O
Pacific	O
and	O
compared	O
the	O
results	O
to	O
vector	O
empirical	O
orthogonal	O
function	O
results	O
.	O
</s>
<s>
 [ 2002a ] 	O
used	O
HHT	O
to	O
determine	O
the	O
dispersion	O
curves	O
of	O
seismic	O
surface	O
waves	O
and	O
compared	O
their	O
results	O
to	O
Fourier-based	O
time-frequency	B-Algorithm
analysis	I-Algorithm
.	O
</s>
<s>
Barnhart	O
and	O
Eichinger	O
 [ 2010 ] 	O
used	O
HHT	O
to	O
extract	O
the	O
periodic	O
components	O
within	O
sunspot	B-Application
data	O
,	O
including	O
the	O
11-year	O
Schwabe	O
,	O
22-year	O
Hale	O
,	O
and	O
~	O
100-year	O
Gleissberg	O
cycles	O
.	O
</s>
<s>
 [ 2003 ] 	O
illustrate	O
the	O
feasibility	O
of	O
the	O
HHT	O
as	O
a	O
signal	O
processing	O
tool	O
for	O
locating	O
an	O
anomaly	O
in	O
the	O
form	O
of	O
a	O
crack	B-Application
,	O
delamination	O
,	O
or	O
stiffness	O
loss	O
in	O
beams	O
and	O
plates	O
based	O
on	O
physically	O
acquired	O
propagating	O
wave	O
signals	O
.	O
</s>
<s>
The	O
authors	O
did	O
extensive	O
investigation	O
into	O
the	O
spline	B-Algorithm
interpolation	I-Algorithm
.	O
</s>
<s>
They	O
also	O
performed	O
a	O
parametric	B-General_Concept
study	I-General_Concept
on	O
the	O
proposed	O
improvement	O
and	O
showed	O
significant	O
improvement	O
in	O
the	O
overall	O
EMD	O
computations	O
.	O
</s>
<s>
They	O
also	O
outline	O
outstanding	O
open	O
problems	O
with	O
HHT	O
,	O
which	O
include	O
:	O
End	O
effects	O
of	O
the	O
EMD	O
,	O
Spline	B-Algorithm
problems	O
,	O
Best	O
IMF	O
selection	O
and	O
uniqueness	O
.	O
</s>
