Page 163 - Fundamentals of Communications Systems

Analog Communications Basics 5.3

signals have been characterized in Chapter 2 and these results will be used
through the remainder of the text. The time average signal power will be an
important characteristic of a message signal.

Definition 5.1 The time average message power, P m ,is
P m = lim P m (T m ) (5.1)
T m →∞
where P m (T m ) is defined in (2.54).

Other characteristics of the message signal that are important include
■ The largest value of the message signal, max m(t)
■ The smallest value of the message signal, min m(t)
d
■ The maximum rate of change of the message signal, max | m(t)|
dt
A characteristic often used to characterize communication signals is the peak
to average power ratio (PAPR).

Definition 5.2 The peak power to average power ratio of m(t)is
(max |m(t)|) 2
PAPR m = (5.2)
P m
The remainder of this book will consistently relate performance of communica-
tion systems back to these parameters that describe the message signal.

EXAMPLE 5.1
Recall the example from Chapter 2 of a filtered computer generated voice saying the
word “Bingo” whose time waveform is shown in Figure 2.1 and whose energy spectrum
is shown in Figure 2.8. This is pretty typical of a spoken word signal that would be
communicated in an analog communication system. A spoken word signal typically has
the characteristic that there is little DC value for the signal and this is reflected in the
notch in the energy spectrum of this signal at 0 Hz. This characteristic implies that
a spoken word signal will pass through a DC block with little distortion. Examining
this signal both the 40 dB bandwidth and 98% energy bandwidth are about 2.5 kHz so
when this signal is used in future examples it will be assumed that W = 2.5 kHz. In
general, spoken word signals have been characterized as having a bandwidth of about
W = 3.5–4 kHz and many commonly employed communication systems are built on this
premise (e.g., the public telephone system).

EXAMPLE 5.2
High quality audio signals have different characteristics than spoken word signals.
Figure 5.3(a) shows the time signal of a short excerpt from a song by Andrea Bocelli
sampled at 44100 Hz. Figure 5.3(b) shows the measured power spectrum from this same
song. This is pretty typical of a high fidelity audio signal that would be communicated