Chapter 3
Data and Signals
3.1 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
3-3 DIGITAL SIGNALS
In addition to being represented by an analog signal,
information can also be represented by a digital signal.
For example, a 1 can be encoded as a positive voltage
and a 0 as zero voltage. A digital signal can have more
than two levels. In this case, we can send more than 1 bit
for each level.
Topics discussed in this section:
Bit Rate
Bit Length
Digital Signal as a Composite Analog Signal
Application Layer
3.2
Figure 3.16 Two digital signals: one with two signal levels and the other
with four signal levels
3.3
Example 3.16
A digital signal has eight levels. How many bits are
needed per level? We calculate the number of bits from
the formula
Each signal level is represented by 3 bits.
3.4
Figure 3.17 The time and frequency domains of periodic and nonperiodic
digital signals
3.5
Figure 3.18 Baseband transmission
A digital signal is a composite analog
signal with an infinite bandwidth.
3.6
Figure 3.19 Bandwidths of two low-pass channels
3.7
Figure 3.20 Baseband transmission using a dedicated medium
3.8
Note
Baseband transmission of a digital
signal that preserves the shape of the
digital signal is possible only if we have
a low-pass channel with an infinite or
very wide bandwidth.
3.9
Figure 3.23 Bandwidth of a bandpass channel
3.10
Note
If the available channel is a bandpass
channel, we cannot send the digital
signal directly to the channel;
we need to convert the digital signal to
an analog signal before transmission.
3.11
Figure 3.24 Modulation of a digital signal for transmission on a bandpass
channel
3.12
3-4 TRANSMISSION IMPAIRMENT
Signals travel through transmission media, which are not
perfect. The imperfection causes signal impairment. This
means that the signal at the beginning of the medium is
not the same as the signal at the end of the medium.
What is sent is not what is received. Three causes of
impairment are attenuation, distortion, and noise.
Topics discussed in this section:
Attenuation
Distortion
Noise
3.13
Figure 3.25 Causes of impairment
3.14
Attenuation
Means loss of energy -> weaker
signal
When a signal travels through a
medium it loses energy overcoming
the resistance of the medium
Amplifiers are used to compensate
for this loss of energy by
amplifying the signal.
3.15
Measurement of
Attenuation
To show the loss or gain of
energy the unit “decibel” is
used.
dB = 10log10P2/P1
P1 - input signal
P2 - output signal
3.16
Figure 3.26 Attenuation
3.17
Example 3.26
Suppose a signal travels through a transmission medium
and its power is reduced to one-half. This means that P 2
is (1/2)P1. In this case, the attenuation (loss of power)
can be calculated as
A loss of 3 dB (–3 dB) is equivalent to losing one-half
the power.
3.18
Example 3.27
A signal travels through an amplifier, and its power is
increased 10 times. This means that P2 = 10P1 . In this
case, the amplification (gain of power) can be calculated
as
3.19
Example 3.28
One reason that engineers use the decibel to measure the
changes in the strength of a signal is that decibel
numbers can be added (or subtracted) when we are
measuring several points (cascading) instead of just two.
In Figure 3.27 a signal travels from point 1 to point 4. In
this case, the decibel value can be calculated as
3.20
Figure 3.27 Decibels for Example 3.28
3.21
Example 3.30
The loss in a cable is usually defined in decibels per
kilometer (dB/km). If the signal at the beginning of a
cable with −0.3 dB/km has a power of 2 mW, what is the
power of the signal at 5 km?
Solution
The loss in the cable in decibels is 5 × (−0.3) = −1.5 dB.
We can calculate the power as
3.22
Distortion
Means that the signal changes its
form or shape
Distortion occurs in composite
signals
Each frequency component has its own
propagation speed traveling through a
medium.
The different components therefore
arrive with different delays at the
receiver.
That means that the signals have
different phases at the receiver than
they did at the source.
3.23
Figure 3.28 Distortion
3.24
Noise
There are different types of
noise
Thermal - random noise of electrons
in the wire creates an extra signal
Induced - from motors and appliances,
devices act are transmitter antenna
and medium as receiving antenna.
Crosstalk - same as above but between
two wires.
Impulse - Spikes that result from
power lines, lighning, etc.
3.25
Figure 3.29 Noise
3.26
Signal to Noise Ratio
(SNR)
To measure the quality of a
system the SNR is often used. It
indicates the strength of the
signal wrt the noise power in the
system.
It is the ratio between two
powers.
It is usually given in dB and
referred to as SNRdB.
3.27
Example 3.31
The power of a signal is 10 mW and the power of the
noise is 1 μW; what are the values of SNR and SNRdB ?
Solution
The values of SNR and SNRdB can be calculated as
follows:
SNR = 10mW/ 1 μW = 10,000
SNRdB = 10 log 10 10,000 = 40
3.28
Example 3.32
The values of SNR and SNRdB for a noiseless channel
are
We can never achieve this ratio in real life; it is an ideal.
3.29
Figure 3.30 Two cases of SNR: a high SNR and a low SNR
3.30
