13
6.6
6.8
7
7.2
7.4
7.6
7.8
x 10
4
-3
-2
-1
0
1
2
3
Time
d
a
ta
(
b
lu
e
)
&
N
C
O
p
h
a
s
e
(
re
d
)
NCO phase, continuous phase FSK
2-FSK, center frequency fc = 0,
modulation index h = 0.5
0.9
1
1.1
1.2
1.3
1.4
1.5
x 10
5
-500
-400
-300
-200
-100
0
100
200
300
400
500
Time
D
a
ta
(
b
lu
e
)
&
F
S
K
-m
o
d
u
la
te
d
s
ig
n
a
l
(r
e
d
)
Continuous FSK modulated signal example
FSK modulation is sometimes characterized by the
frequency separation between symbols. The
relationship between modulation index
h
and
frequency separation is f
separation
= 0.5 h f
symbol_clk
M-ary Number M
Transmitted data is grouped into symbols of size 1,
2, or 3 consecutive bits. The size of the symbol
alphabet is thus M = 2, 4 or 8. The packing of serial
data bits into alphabet symbols is such that the
MSB is received first at the DATA_IN serial input.
The mapping between symbol alphabet and
modulation symbol
i
a
is described in the table
below:
Symbol alphabet
Modulation symbol
i
a
2-FSK ‘0’
-1
2-FSK ‘1’
+1
4-FSK “00”
-3
4-FSK “01”
-1
4-FSK “10”
+1
4-FSK “11”
+3
8-FSK “000”
-7
8-FSK “001”
-5
8-FSK “010”
-3
8-FSK “011”
-1
8-FSK “100”
+1
8-FSK “101”
+3
8-FSK “110”
+5
8-FSK “111”
+7
Gaussian Filter
A filter with Gaussian impulse response can be used
as pre-filtering of the symbols prior to the
continuous phase modulation. Its purpose is to
control the modulated signal bandwidth.
The Gaussian filter is characterized by its BT
product (B is the –3 dB bandwidth, T is the symbol
period = 1/f
symbol rate
). The lower the BT product, the
narrower the modulation bandwidth and the higher
the inter-symbol interference.
The filter impulse response is expressed analytically
as:
−
=
2
2
2
2
exp
2
1
)
(
T
t
T
t
h
σ
σ
π
where
BT
π
σ
2
)
2
ln(
=
The impulse response h(t) is further convoluted
with the rectangular waveform representing the
symbol width T. The resulting impulse is illustrated
below for BT = 0.3, 0.5 and 1.0.