<s>
In	O
applied	O
mathematics	O
,	O
the	O
starred	B-Algorithm
transform	I-Algorithm
,	O
or	O
star	B-Algorithm
transform	I-Algorithm
,	O
is	O
a	O
discrete-time	O
variation	O
of	O
the	O
Laplace	O
transform	O
,	O
so-named	O
because	O
of	O
the	O
asterisk	O
or	O
"	O
star	O
"	O
in	O
the	O
customary	O
notation	O
of	O
the	O
sampled	O
signals	O
.	O
</s>
<s>
The	O
starred	B-Algorithm
transform	I-Algorithm
is	O
a	O
convenient	O
mathematical	O
abstraction	O
that	O
represents	O
the	O
Laplace	O
transform	O
of	O
an	O
impulse	O
sampled	O
function	O
,	O
which	O
is	O
the	O
output	O
of	O
an	O
ideal	O
sampler	O
,	O
whose	O
input	O
is	O
a	O
continuous	O
function	O
,	O
.	O
</s>
<s>
The	O
starred	B-Algorithm
transform	I-Algorithm
is	O
similar	O
to	O
the	O
Z	B-Algorithm
transform	I-Algorithm
,	O
with	O
a	O
simple	O
change	O
of	O
variables	O
,	O
where	O
the	O
starred	B-Algorithm
transform	I-Algorithm
is	O
explicitly	O
declared	O
in	O
terms	O
of	O
the	O
sampling	O
period	O
(	O
T	O
)	O
,	O
while	O
the	O
Z	B-Algorithm
transform	I-Algorithm
is	O
performed	O
on	O
a	O
discrete	O
signal	O
and	O
is	O
independent	O
of	O
the	O
sampling	O
period	O
.	O
</s>
<s>
This	O
makes	O
the	O
starred	B-Algorithm
transform	I-Algorithm
a	O
de-normalized	O
version	O
of	O
the	O
one-sided	O
Z-transform	B-Algorithm
,	O
as	O
it	O
restores	O
the	O
dependence	O
on	O
sampling	O
parameterT	O
.	O
</s>
<s>
Then	O
per	O
the	O
convolution	O
theorem	O
,	O
the	O
starred	B-Algorithm
transform	I-Algorithm
is	O
equivalent	O
to	O
the	O
complex	O
convolution	O
of	O
and	O
,	O
hence	O
:	O
</s>
<s>
Given	O
a	O
Z-transform	B-Algorithm
,	O
X(z )	O
,	O
the	O
corresponding	O
starred	B-Algorithm
transform	I-Algorithm
is	O
a	O
simple	O
substitution	O
:	O
</s>
