563489578934

Problems 409
FM
receiver
FM
detector
output
Notch filter
at 19 kHz
A
E
LPF
2m L (t)
m b (t)
C
Analog switches
Narrow BPF
pass 19 kHz
B
PLL
D
LPF
F
2m R (t)
Figure P5–51
★ 5–52 In a communication system, two baseband signals (they may be analog or digital) are transmitted
simultaneously by generating the RF signal
s(t) = m 1 (t) cos v c t + m 2 (t) sin v c t
The carrier frequency is 7.250 MHz. The bandwidth of m 1 (t) is 5 kHz and the bandwidth of m 2 (t)
is 10 kHz.
(a) Evaluate the bandwidth of s(t).
(b) Derive an equation for the spectrum of s(t) in terms of M 1 (f ) and M 2 (f ).
(c) m 1 (t) and m 2 (t) can be recovered (i.e., detected) from s(t) by using a superheterodyne receiver
with two switching detectors. Draw a block diagram for the receiver and sketch the digital
waveforms that are required to operate the samplers. Describe how they can be obtained.
Show that the Nyquist sampling criterion is satisfied. (Hint: See Fig. P5–51.)
★ 5–53 A digital baseband signal consisting of rectangular binary pulses occurring at a rate of 24 kbitss
is to be transmitted over a bandpass channel.
(a) Evaluate the magnitude spectrum for OOK signaling that is keyed by a baseband digital test
pattern consisting of alternating 1’s and 0’s.
(b) Sketch the magnitude spectrum and indicate the value of the first null-to-null bandwidth.
Assume a carrier frequency of 150 MHz.
5–54 Referring to Prob. 5–53 for the case of a random data pattern and OOK signaling, find the PSD and
plot the result. Compare this result with that for the magnitude spectrum obtained in Prob. 5–53.
5–55 Repeat Prob. 5–53 for the case of BPSK signaling.
5–56 Referring to Prob. 5–53 for the case of a random data pattern with BPSK signaling, find the PSD and
plot the result. Compare this result with that for the magnitude spectrum obtained in Prob. 5–55.
★ 5–57 A carrier is angle modulated with a polar baseband data signal to produce a BPSK signal s(t) =
10 cos [v c t + D p m(t)], where m(t) =;1 corresponds to the binary data 10010110. T b = 0.0025 sec
and v c = 1,000p. Using MATLAB, plot the BPSK signal waveform and its corresponding FFT
spectrum for the following digital modulation indices:
(a) h = 0.2.
(b) h = 0.5.
(c) h = 1.0.
5–58 Evaluate the magnitude spectrum for an FSK signal with alternating 1 and 0 data. Assume that
the mark frequency is 50 kHz, the space frequency is 55 kHz, and the bit rate is 2,400 bitss. Find
the first null-to-null bandwidth.