Page 176 - Fundamentals of Communications Systems

5.16 Chapter Five

(d) n = 1 ⇒ f = 2Hz
n = 2 ⇒ f = 6Hz
n = 3 ⇒ f = 10 Hz
Since the bandwidth is limited to 9 Hz, only the first two terms of the
summation will be kept and there are 4 nonzero terms in the Fourier Series

4
m 1 = ··· f = 2 Hz (5.24)
π 2
4
m −1 = ··· f =−2 Hz (5.25)
π 2
4
m 3 = ··· f = 6 Hz (5.26)
9π 2
4
m −3 = ··· f =−6 Hz (5.27)
9π 2
m k = 0 otherwise (5.28)

The message signal is given as

8 8
m(t) = 2 cos(2π(2)t) + 2 cos(2π(6)t) (5.29)
π 9π

1
0.8

0.6
0.4

0.2
m(t) 0

−0.2
−0.4

−0.6
−0.8

−1
−0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5
Time, t, sec
Figure 5.14 The filtered message signal.