34)
With this above information, let??™s use the random input data in Fig. 2.51as an example.
b
2 # 5 kHz
10 kbps
1
MODULATION THEORY 81
t
t
t
Data
I(t)
Q(t)
+1
??“1
+1
??“1
+1
??“1
Tb
Tb
Tb
FIGURE 2.51 Unfiltered complex envelope of BFSK with 1.
The above waveforms can also be better understood using the following signal constellation diagram.
The amount of phase change encountered in a bit time is equal to
(2.35)
So, using the parameters form the previous example, 1, we see there are phase changes
every bit time, which can also be shown as in Fig. 2.52, where we consider the phase changes of the
first two data bits drawn in the previous figure.
In general, the modulation index is an indicator of the amount of phase allowed to change during
a bit time Tb.
p
p # b
2pfd
Rb
2pfd # Tb
As previously shown, when not considering the effects of the premodulation filter, the occupied BW
becomes theoretically infinite because of the sharp phase reversals observed on the I- and Q-channels.
The addition of the premodulation filter slows down the phase transitions and thus makes the transmit
PSD more spectrally compact or efficient. In Fig. 2.53, we consider the effects of including an example
LPF.
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