<s>
The	B-Algorithm
Hilbert	I-Algorithm
spectrum	I-Algorithm
(	O
sometimes	O
referred	O
to	O
as	O
the	B-Algorithm
Hilbert	I-Algorithm
amplitude	I-Algorithm
spectrum	I-Algorithm
)	O
,	O
named	O
after	O
David	O
Hilbert	O
,	O
is	O
a	O
statistical	O
tool	O
that	O
can	O
help	O
in	O
distinguishing	O
among	O
a	O
mixture	O
of	O
moving	O
signals	O
.	O
</s>
<s>
The	O
spectrum	O
itself	O
is	O
decomposed	O
into	O
its	O
component	O
sources	O
using	O
independent	B-Algorithm
component	I-Algorithm
analysis	I-Algorithm
.	O
</s>
<s>
The	O
separation	O
of	O
the	O
combined	O
effects	O
of	O
unidentified	O
sources	O
(	O
blind	B-Application
signal	I-Application
separation	I-Application
)	O
has	O
applications	O
in	O
climatology	O
,	O
seismology	O
,	O
and	O
biomedical	O
imaging	O
.	O
</s>
<s>
The	B-Algorithm
Hilbert	I-Algorithm
spectrum	I-Algorithm
is	O
computed	O
by	O
way	O
of	O
a	O
2-step	O
process	O
consisting	O
of	O
:	O
</s>
<s>
Applying	O
the	O
Hilbert	B-Algorithm
transform	I-Algorithm
to	O
the	O
results	O
of	O
the	O
above	O
step	O
to	O
obtain	O
the	O
instantaneous	O
frequency	O
spectrum	O
of	O
each	O
of	O
the	O
components	O
.	O
</s>
<s>
The	O
Hilbert	B-Algorithm
transform	I-Algorithm
defines	O
the	O
imaginary	O
part	O
of	O
the	O
function	O
to	O
make	O
it	O
an	O
analytic	O
function	O
(	O
sometimes	O
referred	O
to	O
as	O
a	O
progressive	O
function	O
)	O
,	O
i.e.	O
</s>
<s>
With	O
the	O
Hilbert	B-Algorithm
transform	I-Algorithm
,	O
the	O
singular	O
vectors	O
give	O
instantaneous	O
frequencies	O
that	O
are	O
functions	O
of	O
time	O
,	O
so	O
that	O
the	O
result	O
is	O
an	O
energy	O
distribution	O
over	O
time	O
and	O
frequency	O
.	O
</s>
<s>
The	O
Marginal	O
Hilbert	B-Algorithm
Spectrum	I-Algorithm
show	O
the	O
total	O
energy	O
that	O
each	O
frequency	O
value	O
contribute	O
with	O
.	O
</s>
<s>
The	B-Algorithm
Hilbert	I-Algorithm
spectrum	I-Algorithm
has	O
many	O
practical	O
applications	O
.	O
</s>
<s>
One	O
example	O
application	O
pioneered	O
by	O
Professor	O
Richard	O
Cobbold	O
,	O
is	O
the	O
use	O
of	O
the	B-Algorithm
Hilbert	I-Algorithm
spectrum	I-Algorithm
for	O
the	O
analysis	O
of	O
blood	O
flow	O
by	O
pulse	O
Doppler	O
ultrasound	B-Application
.	O
</s>
<s>
Other	O
applications	O
of	O
the	B-Algorithm
Hilbert	I-Algorithm
spectrum	I-Algorithm
include	O
analysis	O
of	O
climatic	O
features	O
,	O
water	O
waves	O
,	O
and	O
the	O
like	O
.	O
</s>
