Basics of signals data communication

 The main function of the physical layer is moving
information in the form of electromagnetic signals
across a transmission media.
 Information can be in the form of data, voice, picture,
and so on.
 Generally the information usable to a person or
application is not in a form that can be transmitted
over a network.

 The information must be converted into a form that
transmission media can accept.
 Transmission media work by conducting energy
along a physical path.
 So a data stream of 1s and 0s must be turned into
energy in the form of electromagnetic signals.
 A signal is the physical representation of a certain
information.

 Signals and data are classified as analog or digital.
 Analog refers to something that is continuous- a
set of data and all possible points between.
 An example of analog data is the human voice.
 Digital refers to something that is discrete –a set of
specific points of data with no other points in
between.
 An example of digital data is data stored in the
memory of a computer in the form of 0s and 1s.

 An analog signal is a continuous wave form
that changes smoothly. As the wave moves
from a value A to a value B, it passes through
and includes an infinite number of values
along its path.
 A digital signal can have only a limited number
of defined values, often as simple as 1 and 0.

Comparison of analog and digital signals
Signals can be analog or digital. Analog signals can have
an infinite number of values in a range; digital signals can
have only a limited number of values.

 Both analog and digital
signals can be of two forms:
periodic and aperiodic
(non-periodic) signals.
 A signal periodic signal
consists a continuously
repeated pattern.
 The completion of one full
pattern is called a cycle.
 A period is defined as the
amount of time (expressed
in seconds) required to
complete one full cycle.

 An aperiodic signal
changes constantly
without exhibiting a
pattern or cycle that
repeats over the time.
 Remark: By using Fourier
Transform it is possible to
decompose an aperiodic
signal into an infinite
number of periodic signals
(see appendix D)

 Analog signals can be
classified as simple or
composite.
 A simple analog signal or
sine wave, cannot be
decomposed into simpler
signals.
 A composite analog signal
is composed of multiple
sine waves.

 Sine waves can be fully described by three
characteristics: amplitude, period, frequency and
phase.
 Amplitude: on a graph, the amplitude of a signal is
the value of the signal at any point on the wave. It
is equal to the vertical distance from a given point
on the wave from the horizontal axis.
 Amplitude is measured
In volts, amperes, or watts,
depending on the type of
Signal.

 Period and Frequency: period refers to the
amount of time, in seconds, a signal needs to
complete one cycle.
 Frequency refers to the number of periods in
one second. The frequency of a signal its
number of cycles per second.
 Frequency is the rate of change with respect to
time. Change in a short span of time means
high frequency. Change over a long span of
time means low frequency.
 If a signal does not change at all, its frequency
is zero. If a signal changes instantaneously, its
frequency is infinite.

Basics of signals data communication

Table 3.1 Units ooff ppeerriiooddss aanndd ffrreeqquueenncciieess
Unit Equivalent Unit Equivalent
Seconds (s) 1 s hertz (Hz) 1 Hz
Milliseconds (ms) 10–3 s kilohertz (KHz) 103 Hz
Microseconds (ms) 10–6 s megahertz (MHz) 106 Hz
Nanoseconds (ns) 10–9 s gigahertz (GHz) 109 Hz
Picoseconds (ps) 10–12 s terahertz (THz) 1012 Hz

 Period is the amount of time it takes a signal to
complete one cycle.
 Frequency is the number of cycles per second.
 Frequency=1/Period
 Period=1/Frequency

EExxaammppllee 11
Express a period of 100 ms in microseconds, and express
the corresponding frequency in kilohertz.
SSoolluuttiioonn
From Table 3.1 we find the equivalent of 1 ms.We make
the following substitutions:
100 ms = 100 ´ 10-3 s = 100 ´ 10-3 ´ 106 ms = 105 ms
Now we use the inverse relationship to find the
frequency, changing hertz to kilohertz
100 ms = 100 ´ 10-3 s = 10-1 s
f = 1/10-1 Hz = 10 ´ 10-3 KHz = 10-2 KHz

 The term phase describes the position of the waveform
relative to time zero.
 The phase is measured in degrees or radians (360 degrees
is 2p radians)

•Time-domain representation
•Frequency-domain representation

Time and frequency domains (continued)

 A single-frequency sine wave is not useful in data
communications; we need to change one or more of its
characteristics to make it useful.
 According to Fourier analysis, any composite signal
can be represented as a combination of simple sine
waves with different frequencies, phases, and
amplitudes.

Note: Direct current (DC) component

 The frequency spectrum of a signal is the collection of
all the component frequencies it contains and is shown
using a frequency-domain graph.
 The bandwidth of a signal is the width of the
frequency spectrum, i.e., bandwidth refers to the range
of component frequencies.
 To compute the bandwidth, subtract the lowest
frequency from the highest frequency of the range.

EExxaammppllee 33
If a periodic signal is decomposed into five sine waves
with frequencies of 100, 300, 500, 700, and 900 Hz,
what is the bandwidth? Draw the spectrum, assuming all
components have a maximum amplitude of 10 V.
SSoolluuttiioonn
B = fh - fl = 900 - 100 = 800 Hz
The spectrum has only five spikes, at 100, 300, 500, 700,
and 900 (see Figure 13.4 )

EExxaammppllee 44
A signal has a bandwidth of 20 Hz. The highest
frequency is 60 Hz. What is the lowest frequency? Draw
the spectrum if the signal contains all integral frequencies
of the same amplitude.
SSoolluuttiioonn
BB == ffhh - ffll
2200 == 6600 - ffll
ffll == 6600 - 2200 == 4400 HHzz

 A medium may pass some
frequencies and may
block others. This means
that when we send a
composite signal,
containing many
frequencies, at one end of
the transmission medium,
we may not receive the
same signal at the other
end.
A digital signal is a composite ssiiggnnaall wwiitthh aann iinnffiinniittee bbaannddwwiiddtthh..

 The range of frequencies that a medium can pass is
called its bandwidth.
 The bandwidth is a property of a medium: It is
difference between the highest and the lowest
frequencies that the medium can satisfactorily pass.
 If bandwidth of a medium does not mach the spectrum
of a signal, some of the frequencies are lost.

EExxaammppllee 55
A signal has a spectrum with frequencies between 1000
and 2000 Hz (bandwidth of 1000 Hz). A medium can
pass frequencies from 3000 to 4000 Hz (a bandwidth of
1000 Hz). Can this signal faithfully pass through this
medium?
SSoolluuttiioonn
TThhee aannsswweerr iiss ddeeffiinniitteellyy nnoo.. AAlltthhoouugghh tthhee ssiiggnnaall ccaann hhaavvee
tthhee ssaammee bbaannddwwiiddtthh ((11000000 HHzz)),, tthhee rraannggee ddooeess nnoott
oovveerrllaapp.. TThhee mmeeddiiuumm ccaann oonnllyy ppaassss tthhee ffrreeqquueenncciieess
bbeettwweeeenn 33000000 aanndd 44000000 HHzz;; tthhee ssiiggnnaall iiss ttoottaallllyy lloosstt..

 Most of the digital signals are aperiodic and, thus
period or frequency is not appropriate.
 Bit interval ( instead of period) and Bit rate (instead
of frequency)
 The bit interval is the time required to send one
single bit.
 The bit rate is the number of bit intervals in one
second, usually expressed in bits per second (bps).

EExxaammppllee 66
A digital signal has a bit rate of 2000 bps. What is the
duration of each bit (bit interval)
SSoolluuttiioonn
The bit interval is the inverse of the bit rate.
Bit interval = 1/ 2000 s = 0.000500 s
= 0.000500 x 106 ms = 500 ms

 A digital signal is a composite signal with an
infinite bandwidth.
 It is possible to send digital data through a
band-limited medium, such as a telephone
line.
 What is the minimum required bandwidth B
in Hertz if we want to send n bps?

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ootthheerr..
•TThhee aannaalloogg bbaannddwwiiddtthh ooff aa mmeeddiiuumm iiss eexxpprreesssseedd iinn
hheerrttzz;; tthhee ddiiggiittaall bbaannddwwiiddtthh,, iinn bbiittss ppeerr sseeccoonndd..
nn<<==22BB (( nn iinn bbppss aanndd BB iinn HHeerrttzz))
Bit
Rate
Harmonic
1
Harmonics
1, 3
Harmonics
1, 3, 5
Harmonics
1, 3, 5, 7
1 Kbps 500 Hz 2 KHz 4.5 KHz 8 KHz
10 Kbps 5 KHz 20 KHz 45 KHz 80 KHz
100 Kbps 50 KHz 200 KHz 450 KHz 800 KHz

Basics of signals data communication

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Basics of signals data communication