Page 217 - Fundamentals of Communications Systems

Amplitude Modulation 6.39

(a) Is the modulation using the upper sideband or the lower sideband?
(b) Find ˆm(t).
Problem 6.29. At the output of a double sideband amplitude modulator (DSB-AM)
the signal
√
x c (t) = 8 cos(200πt) 2 cos(2π f c t) (6.36)

is observed. You know that the input message signal had a power of 2 W.

(a) Find x z (t).
(b) Find x A(t) and x P (t) over t ∈ [0, 0.01].
(c) What is the input message signal and what is A c ?
(d) Plot the Fourier transform of the complex envelope, X z (f ) using impulse
functions. What the bandpass bandwidth, B T , that this signal occupies?

Problem 6.30. Consider the DSB-AM signal from the previous problem given as
√
x c (t) = 8 cos(200πt) 2 cos(2π f c t) (6.37)

This signal is put into a bandpass filter which has a complex envelope charac-
terized with

0.5 f
⎧
⎨
1 − | f |≤ 200
H Q (f ) = 0 H I (f ) = 100 (6.38)
0 elsewhere
⎩
The output of the filter at bandpass is denoted y c (t) and at baseband is denoted
y z (t).
(a) Find and plot H c (f ).
(b) Find y z (t).
(c) Find y A(t) and y P (t) over t ∈ [0, 0.01]. Why is the phase varying as a function
of time for the DSB-AM signal?
Problem 6.31. A message signal with an energy spectrum given in Figure 6.35
is to be transmitted with single sideband amplitude modulation (SSB-AM).
Additionally, min(m(t)) =−2 and P m = 10.

(a) Specify the quadrature filter transfer function to achieve a lower sideband
transmission.
.
(b) Find the transmitted power, P x z
(c) Plot the modulator output spectrum (either bandpass or baseband is fine)
and compute the E B .