Page 212 - Fundamentals of Communications Systems

6.34 Chapter Six

xt ()
I

+
(
2 cos 2π f t) Σ xt ()
c
c
−
π 2
x t ()
Q

Figure 6.37 A quadrature upconverter.

2
2
(c) If |X c ( f c + f m )| = 100|X c ( f c − f m )| what is the value of θ that would
produce this spectrum.
(d) Postulate why this test is known as a single sideband rejection test.
Problem 6.13. A message with a Fourier transform of

1 π f
√ sin −W ≤ f ≤ W
W W
M(f ) = (6.34)
0 elsewhere
is to be transmitted with a quadrature modulation.
(a) Calculate the message energy, E m .
.
(b) For SSB-AM (upper sideband) compute the output transmitted energy, E x z
(c) Design a simple quadrature filter for VSB-AM where f v = W/4. Give either
H Q (f )or H z (f ).
, in part c). Note,
(d) Compute the resulting output energy for your design, E x z
depending on your design the solution might be easiest done with the aid of
a computer
Problem 6.14. (UM). An amplitude modulated (AM) signal has the following form

x c (t) = [A+ 1.5 cos(10πt) − 3.0 cos(20πt)] cos(2π f c t)

where the message signal is

m(t) = cos(10πt) − 2.0 cos(20πt)

(a) What type of amplitude modulation is this?
(b) What is the spectrum of x c (t), X c (f )?