Page 174 - Fundamentals of Communications Systems

5.14 Chapter Five

mt () Hf () m t Amt () + N t ()
√() =
L
R
Figure 5.12 An example of filtering a message signal.

is input into the system shown in Figure 5.12 where
2π500
H R (f ) = (5.17)
j 2π f + 2π500
(a) Find and plot the output signal.
(b) If ˆm(t) = Am(t) + n L (t) for a chosen value of Afind the power of the distortion
n L (t).
(c) Find the value of A that minimizes the distortion power.
(d) Redesign H R (f ) to reduce the effective distortion power.

Problem 5.5. A message signal is of the form
m(t) = 2 cos(4πt) + cos(6πt)

A plot of the message signal is given in Figure 5.13.

4

3

2

1
m(t)

0

−1

−2

−3
0 0.5 1 1.5 2 2.5 3
Time, t, sec
Figure 5.13 The message signal for Problem 5.5.