Page 205 - Fundamentals of Communications Systems

Amplitude Modulation 6.27

100 Hz. The modulated signal has been greatly attenuated in y L (t) while the tone used
in demodulation is clearly evident. For example, in a channel with τ p = 45.3 µs a phase
◦
shift of −114 occurs. The measured phase of the output tone is shown in Figure 6.30(b)
and it is close to −114 once the filter transients have passed. The imperfections in the
◦
filter can be seen to allow the message signal to cause some phase jitter to be induced on
the demodulator reference but the overall system produces a high quality audio output.

Noncoherent demodulation (envelope detection) is also used in conjunction
with a large carrier version of VSB-AM in analog television reception in the
United States. The details of how this is possible with a quadrature modulation
will be addressed in the homework.

6.3.5 Quadrature Modulation Conclusions
Quadrature modulation provides better spectral efficiency than either DSB-AM
or LC-AM but with a more complex modulator. Quadrature modulation accom-
plishes this improved spectral efficiency by using the imaginary portion of the
complex envelope. Like LC-AM, VSB-AM wastes part of the transmitted power
(the imaginary component is not used in demodulation) but for a useful purpose.
LC-AM contains a carrier signal that transmits no information while VSB-AM
transmits a filtered signal in the quadrature component of the modulation but
never uses this signal in demodulation. VSB-AM is also suitable for use with a
large carrier and envelope detection (this is what is used in broadcast TV) and
this idea will be explored in the homework.
In conclusion, three types of amplitude modulated signals have been pre-
sented in this chapter. These three signaling schemes provide different options
in cost/bandwidth efficiency tradeoffs.

6.4 Homework Problems
Problem 6.1. The message signal in a DSB-AM system is of the form
m(t) = 12 cos(6πt) + 3 cos(10πt)

(a) Calculate the message power, P m .
(b) If this message is DSB-AM modulated on a carrier with amplitude A c ,
calculate the Fourier series of x z (t).
(c) Assuming f c = 20 Hz calculate the Fourier series of x c (t) and plot the
resulting time waveform when A c = 1.
.
(d) Compute the output power of the modulated signal, P x c
(e) Calculate and plot x P (t). Computer might be useful.

Problem 6.2. A message signal of the form
m(t) = cos(2π f m t)
is to be transmitted by DSB-AM with a carrier frequency f c .