Page 51 - Fundamentals of Communications Systems

Signals and Systems Review 2.3

0.8

0.6

0.4

0.2

0
x(t)
−0.2

−0.4

−0.6

−0.8

−1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Time, seconds
Figure 2.1 The time waveform for a computer-generated voice saying “Bingo.”

EXAMPLE 2.4

x(t) = cos(2π f c t)
T m /2
1 2
P x = lim cos (2π f c t)dt
T m →∞ T m
−T m /2
T m /2
1 1 1 1

= lim + cos(4π f c t) dt = (2.6)
T m →∞ T m 2 2 2
−T m /2
EXAMPLE 2.5
The waveform in Figure 2.2 is an analytical representation of the transmitted signal
in a simple radar or sonar system. A signal pulse is transmitted for τ seconds and the
receiver then listens for T seconds for returns from airplanes, ships, stormfronts, or
other targets. After T seconds another pulse is transmitted. For this signal

1 T m /2 2 1 τ τ
P x = lim |x(t)| dt = dt = (2.7)
T m →∞ T m T T
−T m /2 0