563489578934

Sec. 2–9 Bandwidth of Signals 111
where the spectrum has a maximum value at f = f c . With the use of these two equations,
Eq. (2–202) becomes
A(f) = -10 log 10 c
4000 (f)
B eq (f c ) d
(2–205)
where A(f) is the decibel attenuation of power measured in a 4-kHz band at frequency f compared
with the total average power level of the signal. For the case of BPSK signaling, using Eq.
(2–201), we find that the decibel attenuation is
A(f) = -10 log 10 e 4000
(2–206)
R c sin pT b(f - f c )
2
d f
pT b (f - f c )
where R = 1/T b is the data rate. If we attempt to find the value of R such that A(f) will fall below
the specified FCC spectral envelope shown in Fig. 2–24 (B = 30 MHz), we will find that R
is so small that there will be numerous zeros in the (sin x)/x function of Eq. (2–206) within the
desired frequency range, -50 MHz 6 (f - f c ) 6 50 MHz. This is difficult to plot, so by
30 MHz
A(f)
(dB)
30
P 4kHz (f)
A(f) = –10 log10 –––––––––
P total
(
(
40
50
FCC envelope for B = 30 MHz
[Eq. (2–193)]
Quasi-bandlimited MSK signaling
for R = 25 Mbit/s
[Amoroso, 1980]
70
80
90
BPSK envelope for
R=0.0171 Mbits/s
[Eq. (2–206)]
–50 –40 –30 –20 –10 0 10 20 30 40 50
f = f – f c (MHz)
Figure 2–24 FCC-allowed envelope for B = 30 MHz.