Cryptography Reference
In-Depth Information
Putting:
t
q
(
t
)=
g
(
τ
)
dτ
0
and for considerations of normalization, by imposing that:
q
(
t
)=
1
2
if
t
≥
LT
the phase
φ
(
t
)
on the interval
[
iT,
(
i
+1)
T
[
is equal to:
i
i−L
φ
(
t
)=2
πh
a
n
q
(
t
−
nT
)+
πh
a
n
(2.39)
n
=
i
−
L
+1
n
=
−∞
When
L
=1
, the continuous phase frequency modulations are said to be
full
response
whereas for
L>
1
,theyaresaidtobe
partial response
.
To illustrate continuous phase-frequency-shift keying, we are going to con-
sider three examples,
Minimum Shift Keying
(MSK) modulation,
L-ary Raised
Cosine
(LRC) modulation and
Gaussian Minimum Shift Keying
(GMSK) mod-
ulation.
Continuous phase-frequency-shift keying with modulation
index
h
=1
/
2
: Minimum Shift Keying (MSK)
For this modulation, the index
h
is equal to
1
/
2
and the symbols
a
i
are binary
(
1
). The function
g
(
t
)
is a rectangular pulse of amplitude
1
/
2
T
and width
T
.
Thus the function
q
(
t
)
is equal to:
±
q
(
t
)= 0
t
≤
0
t
2
T
q
(
t
)=
0
≤
t
≤
T
(2.40)
q
(
t
)=
2
t
≥
T
MSK modulation is full response continuous phase frequency shift keying mod-
ulation (
L
=1
).
On the interval
[
iT,
(
i
+1)
T
[
, the phase
φ
(
t
)
of the MSK signal has the
expression:
i
−
1
φ
(
t
)=
π
2
a
i
(
t
−
iT
)
+
π
2
a
n
(2.41)
T
n
=
−∞
The evolution of the phase
φ
(
t
)
as a function of time is shown in Figure 2.10.
We can note that the phase
φ
(
t
)
varies linearly over a time interval
T
and that
there is no discontinuity at instants
iT
.
