Page 209 - Fundamentals of Communications Systems

Amplitude Modulation 6.31

system), at a center frequency of f c Hz. Station B is broadcasting a 1 V peak
3 kHz square wave, m B (t), at f c + 30 kHz with no filtering at the transmitter.
Since each transmitted waveform will have a different propagation loss, the
received waveform is given by the form
√
r c (t) = A A [(1.5 + m A (t)) 2 cos(2π f c t + φ A )]
√
+ A B [(1.5 + m B (t)) 2 cos(2π( f c + 30000)t + φ B )]

Assume without loss of generality that the phase shift for the station A is zero,
i.e., φ A = 0.

(a) Give the complex envelope of the received signal, r z (t).
(b) Find the spectrum (Fourier series coefficients) of the complex envelope, r z (t).
(c) The demodulator has an ideal bandpass filter with a center frequency of
f c and a two-sided bandwidth of 2 W = 15 kHz followed by an envelope
detector as shown in Figure 6.33. Plot the output demodulated waveform,
ˆ m A (t), over 5 ms of time for several values of φ b in the range [0, 2π] and
A B = 0.1, 1, 10.
The distortion you see in this example is called adjacent channel interference
and one of the FCC’s functions is to regulate the amount of interference each
station produces for people trying to receive another station.

Problem 6.8. Consider the message signal in Figure 6.34 and a bandpass signal
of the form
√
x c (t) = (5 + bm(t)) 2 cos(2π f c t)
(a) What sort of modulation is this?
1
(b) Plot the bandpass signal, x c (t), with b = 2 when f c .
T
(c) How big can b be and still permit envelope detection for distortion-free
message signal recovery.
(d) Compute the transmitted power for b = 3.
(e) Compute MCPR for b = 3.

mt ()

1
− T T
… −T 2 2 …
t

−1
Figure 6.34 A message signal for Problem 6.8.