<s>
In	O
electronics	O
and	O
telecommunications	O
,	O
pulse	B-Algorithm
shaping	I-Algorithm
is	O
the	O
process	O
of	O
changing	O
a	O
transmitted	O
pulses	B-Algorithm
 '	O
waveform	O
to	O
optimize	O
the	O
signal	O
for	O
its	O
intended	O
purpose	O
or	O
the	O
communication	O
channel	O
.	O
</s>
<s>
This	O
is	O
often	O
done	O
by	O
limiting	O
the	O
bandwidth	B-Algorithm
of	O
the	O
transmission	O
and	O
filtering	O
the	O
pulses	B-Algorithm
to	O
control	O
intersymbol	O
interference	O
.	O
</s>
<s>
Pulse	B-Algorithm
shaping	I-Algorithm
is	O
particularly	O
important	O
in	O
RF	O
communication	O
for	O
fitting	O
the	O
signal	O
within	O
a	O
certain	O
frequency	O
band	O
and	O
is	O
typically	O
applied	O
after	O
line	B-Protocol
coding	I-Protocol
and	O
modulation	B-Application
.	O
</s>
<s>
Transmitting	O
a	O
signal	O
at	O
high	O
modulation	B-Application
rate	O
through	O
a	O
band-limited	O
channel	O
can	O
create	O
intersymbol	O
interference	O
.	O
</s>
<s>
The	O
reason	O
for	O
this	O
are	O
Fourier	O
correspondences	O
(	O
see	O
Fourier	B-Algorithm
transform	I-Algorithm
)	O
.	O
</s>
<s>
A	O
bandlimited	O
signal	O
corresponds	O
to	O
an	O
infinite	O
time	O
signal	O
,	O
that	O
causes	O
neighbouring	O
pulses	B-Algorithm
to	O
overlap	O
.	O
</s>
<s>
As	O
the	O
modulation	B-Application
rate	O
increases	O
,	O
the	O
signal	O
's	O
bandwidth	B-Algorithm
increases	O
.	O
</s>
<s>
As	O
soon	O
as	O
the	O
spectrum	O
of	O
the	O
signal	O
is	O
a	O
sharp	O
rectangular	O
,	O
this	O
leads	O
to	O
a	O
sinc	B-Algorithm
shape	O
in	O
the	O
time	O
domain	O
.	O
</s>
<s>
This	O
happens	O
if	O
the	O
bandwidth	B-Algorithm
of	O
the	O
signal	O
is	O
larger	O
than	O
the	O
channel	O
bandwidth	B-Algorithm
,	O
leading	O
to	O
a	O
distortion	O
.	O
</s>
<s>
Theoretically	O
for	O
sinc	B-Algorithm
shaped	O
pulses	B-Algorithm
,	O
there	O
is	O
no	O
ISI	O
,	O
if	O
neighbouring	O
pulses	B-Algorithm
are	O
perfectly	O
aligned	O
,	O
i.e.	O
</s>
<s>
The	O
signal	O
's	O
spectrum	O
is	O
determined	O
by	O
the	O
modulation	B-Application
scheme	O
and	O
data	O
rate	O
used	O
by	O
the	O
transmitter	O
,	O
but	O
can	O
be	O
modified	O
with	O
a	O
pulse	B-Algorithm
shaping	I-Algorithm
filter	O
.	O
</s>
<s>
This	O
pulse	B-Algorithm
shaping	I-Algorithm
will	O
make	O
the	O
spectrum	O
smooth	O
,	O
leading	O
to	O
a	O
time	O
limited	O
signal	O
again	O
.	O
</s>
<s>
Usually	O
the	O
transmitted	O
symbols	O
are	O
represented	O
as	O
a	O
time	O
sequence	O
of	O
dirac	O
delta	O
pulses	B-Algorithm
multiplied	O
with	O
the	O
symbol	O
.	O
</s>
<s>
At	O
this	O
point	O
,	O
the	O
bandwidth	B-Algorithm
of	O
the	O
signal	O
is	O
unlimited	O
.	O
</s>
<s>
This	O
theoretical	O
signal	O
is	O
then	O
filtered	O
with	O
the	O
pulse	B-Algorithm
shaping	I-Algorithm
filter	O
,	O
producing	O
the	O
transmitted	O
signal	O
.	O
</s>
<s>
If	O
the	O
pulse	B-Algorithm
shaping	I-Algorithm
filter	O
is	O
a	O
rectangular	O
in	O
the	O
time	O
domain	O
(	O
like	O
this	O
is	O
usually	O
done	O
when	O
drawing	O
it	O
)	O
,	O
this	O
would	O
lead	O
to	O
an	O
unlimited	O
spectrum	O
.	O
</s>
<s>
In	O
many	O
base	O
band	O
communication	O
systems	O
the	O
pulse	B-Algorithm
shaping	I-Algorithm
filter	O
is	O
implicitly	O
a	O
boxcar	O
filter	O
.	O
</s>
<s>
Its	O
Fourier	B-Algorithm
transform	I-Algorithm
is	O
of	O
the	O
form	O
sin(x )	O
/x	O
,	O
and	O
has	O
significant	O
signal	O
power	O
at	O
frequencies	O
higher	O
than	O
symbol	O
rate	O
.	O
</s>
<s>
This	O
is	O
not	O
a	O
big	O
problem	O
when	O
optical	B-Architecture
fibre	I-Architecture
or	O
even	O
twisted	O
pair	O
cable	O
is	O
used	O
as	O
the	O
communication	O
channel	O
.	O
</s>
<s>
However	O
,	O
in	O
RF	O
communications	O
this	O
would	O
waste	O
bandwidth	B-Algorithm
,	O
and	O
only	O
tightly	O
specified	O
frequency	O
bands	O
are	O
used	O
for	O
single	O
transmissions	O
.	O
</s>
<s>
Therefore	O
,	O
better	O
filters	O
have	O
been	O
developed	O
,	O
which	O
attempt	O
to	O
minimise	O
the	O
bandwidth	B-Algorithm
needed	O
for	O
a	O
certain	O
symbol	O
rate	O
.	O
</s>
<s>
An	O
example	O
in	O
other	O
areas	O
of	O
electronics	O
is	O
the	O
generation	O
of	O
pulses	B-Algorithm
where	O
the	O
rise	O
time	O
need	O
to	O
be	O
short	O
;	O
one	O
way	O
to	O
do	O
this	O
is	O
to	O
start	O
with	O
a	O
slower-rising	O
pulse	O
,	O
and	O
decrease	O
the	O
rise	O
time	O
,	O
for	O
example	O
with	O
a	O
step	O
recovery	O
diode	O
circuit	O
.	O
</s>
<s>
To	O
understand	O
this	O
completely	O
,	O
one	O
needs	O
the	O
Hilbert	B-Algorithm
transform	I-Algorithm
,	O
that	O
induces	O
a	O
direction	O
by	O
the	O
convolution	O
with	O
the	O
Cauchy	O
Kernel	O
.	O
</s>
<s>
Not	O
every	O
filter	O
can	O
be	O
used	O
as	O
a	O
pulse	B-Algorithm
shaping	I-Algorithm
filter	O
.	O
</s>
<s>
Examples	O
of	O
pulse	B-Algorithm
shaping	I-Algorithm
filters	O
that	O
are	O
commonly	O
found	O
in	O
communication	O
systems	O
are	O
:	O
</s>
<s>
Sender	O
side	O
pulse	B-Algorithm
shaping	I-Algorithm
is	O
often	O
combined	O
with	O
a	O
receiver	O
side	O
matched	O
filter	O
to	O
achieve	O
optimum	O
tolerance	O
for	O
noise	O
in	O
the	O
system	O
.	O
</s>
<s>
In	O
this	O
case	O
the	O
pulse	B-Algorithm
shaping	I-Algorithm
is	O
equally	O
distributed	O
between	O
the	O
sender	O
and	O
receiver	O
filters	O
.	O
</s>
<s>
Other	O
approaches	O
that	O
eliminate	O
complex	O
pulse	B-Algorithm
shaping	I-Algorithm
filters	O
have	O
been	O
invented	O
.	O
</s>
<s>
In	O
OFDM	B-Protocol
,	O
the	O
carriers	O
are	O
modulated	B-Application
so	O
slowly	O
that	O
each	O
carrier	O
is	O
virtually	O
unaffected	O
by	O
the	O
bandwidth	B-Algorithm
limitation	O
of	O
the	O
channel	O
.	O
</s>
<s>
Theoretically	O
the	O
best	O
pulse	B-Algorithm
shaping	I-Algorithm
filter	O
would	O
be	O
the	O
sinc	B-Algorithm
filter	O
,	O
but	O
it	O
cannot	O
be	O
implemented	O
precisely	O
.	O
</s>
<s>
It	O
is	O
a	O
non-causal	B-Algorithm
filter	I-Algorithm
with	O
relatively	O
slowly	O
decaying	O
tails	O
.	O
</s>
<s>
Raised-cosine	O
is	O
similar	O
to	O
sinc	B-Algorithm
,	O
with	O
the	O
tradeoff	O
of	O
smaller	O
sidelobes	O
for	O
a	O
slightly	O
larger	O
spectral	O
width	O
.	O
</s>
<s>
They	O
have	O
a	O
configurable	O
excess	O
bandwidth	B-Algorithm
,	O
so	O
communication	O
systems	O
can	O
choose	O
a	O
trade	O
off	O
between	O
a	O
simpler	O
filter	O
and	O
spectral	O
efficiency	O
.	O
</s>
