Cryptography Reference
In-Depth Information
Figure 2.11 - Power spectral density of the complex envelope of MSK and 4-PSK
signals.
modulation for
fT
=1
.
2
whereas for a
4
RC
(
h
=1
/
2
,
a
i
=
±
1)
modulation,
this level is reached for
fT
=0
.
7
.
The function
q
(
t
)
is equal to:
t
2
LT
−
4
π
sin
2
πt
1
q
(
t
)=
0
≤
t
≤
LT
LT
(2.51)
1
2
=
t>LT
Gaussian minimum shift keying modulation (GMSK)
The index
h
of this modulation is equal to
1
/
2
and the symbols
a
i
are binary
(
±
1)
. The function
g
(
t
)
is defined as follows:
g
(
t
)=
h
(
t
)
∗
χ
(
t
)
(2.52)
where
h
(
t
)
is a rectangular pulse of amplitude
1
/T
(
T
=
T
b
)
on the interval
[
T/
2
,T/
2]
and
χ
(
t
)
is the impulse response of a Gaussian filter with passband
at -3 dB equal to
B
g
:
χ
(
t
)=
2
π
−
2
π
2
B
g
t
2
)
/
ln 2
ln 2
B
g
exp(
−
(2.53)
After resolution of the convolution product, the function
g
(
t
)
canbewrittenin
the form:
erf
πB
g
2
2
)
erf
πB
g
2
2
)
1
2
T
ln 2
(
t
+
T
T
g
(
t
)=
−
ln 2
(
t
−
(2.54)
