Cryptography Reference
In-Depth Information
where
s
e
(
t
)
is the complex envelope of the signal
S
(
t
)
with:
s
e
(
t
)=
A
i
a
i
h
(
t
−
iT
)
(2.12)
Taking into account the fact that the data
d
i
provided by the source of infor-
mation are
iid
, the modulation symbols
a
i
are independent, with zero mean and
variance equal to
(
M
2
1)
/
3
.
It can be shown that the power spectral density (psd) of the signal
S
(
t
)
is
equal to:
−
γ
S
(
f
)=
1
f
0
)+
1
4
γ
s
e
(
f
−
4
γ
s
e
(
f
+
f
0
)
(2.13)
with:
A
2
T
sin
πfT
πfT
2
γ
s
e
(
f
)=
M
2
−
1
(2.14)
3
The psd of
s
e
(
t
)
expressed in dB is shown in Figure 2.3 as a function of the
normalized frequency
fT
,for
M
=4
and
A
2
T
=1
.
Figure 2.3 - Power spectral density (psd) of the complex envelope of a signal ASK-4,
with
A
2
T
=1
.
The psd of
S
(
t
)
is centred on the frequency carrier
f
0
and its envelope
decreases in
f
2
. It is made up of a main lobe of width
2
/T
and of sidelobes that
periodically have zero crossing at
f
0
±
k/T
.
Note
The bandwidth is, strictly speaking, infinite. In practice, we can decide only
to transmit a percentage of the power of the signal
S
(
t
)
and in this case, the
