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3.1
Chapter 3Data and Signals
Part 1
Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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3.2
To be transmitted, data must be
transformed to electromagnetic signals.
Note
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3.3
Terms & Concepts
Data - Logical
Signal - Physical
Channel - Logical
Link Physical (carr ies one or more channels)
Bit Rate (N) (bi t per second) - Data
Bandwidth (B) (H z cycle per second) Signal and Channel
Capacity (C) (bit per second) - Channel
Signal E lement - Physical
Signal Rate (S) (Baud Rate)Data Element - Logical
Data Rate (N)
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3.4
Data & Signals
Data
Analog Digital
Signal
Analog
Digital
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3.5
3
-
1 ANALOG AND DIGITAL
Data
can
be
analog
or
digital
.
The
term
analog
data
refers
to
information
that
is
continuous
;
digital
data
refers
toinformation
that
has
discrete
states
.
Analog
data
take
on
continuous
values
.
Digital
data
take
on
discrete
values
.
Analog and Digital Data
Analog and Digital Signals
Periodic and Nonperiodic Signals
Topics discussed in this section:
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3.6
Note
Data can be analog or digital.
Analog data are continuous and take
continuous values.
Digital data have discrete states and
take discrete values.
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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.
Note
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Figure 3.2 Comparison of analog and digi tal signals
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In data communications, we commonly
use periodic analog signals andnonperiodic digital signals.
Note
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3-2 PERIODIC ANALOG SIGNALS
Periodicanalogsignalscanbeclassif iedassimpleor
composite.Asimpleper iodicanalogsignal,asinewave,cannotbedecomposedintosimplersignals.Acomposite
periodicanalogsignal iscomposedofmultiplesine
waves.
Sine Wave
WavelengthTime and Frequency Domain
Composite Signals
Bandwidth
Topics discussed in this section:
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Figure 3.3 A sine wave
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We discuss a mathematical approach tosine waves in Appendix E online.
Note
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The power in your house can be represented by a sine
wave with a peak amplitude of 155 to 170 V. However, it
is common knowledge that the voltage of the power in
U.S. homes is 110 to 120 V. This discrepancy is due to
the fact that these areroot mean square(rms) values.
The signal is squared and then the average amplitude is
calculated. The peak value is equal to2rmsvalue.
Example 3.1
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Figure 3.4 Two signals with the same phase and f requency,but di ff erent amplitudes
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The voltage of a battery is a constant; this constant value
can be considered a sine wave, as we wil l see later. For
example, the peak value of anAAbattery is normally
1.5 V.
Example 3.2
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Frequency and period are the inverse ofeach other.
Note
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3.19
The power we use at home has a f requency of60 Hz.
The per iod of this sine wave can be determined as
follows:
Example 3.3
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3.20
Express a per iod of 100 ms in microseconds.
Example 3.4
Solution
From Table 3.1 we f ind the equivalents of 1 ms (1 ms is103s) and 1 s (1 s is 106s). We make the following
substitutions:.
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3.21
The per iod of a signal is 100 ms. What is its frequency inkilohertz?
Example 3.5
Solution
First we change 100 ms to seconds, and then we
calculate the frequency from the per iod (1 Hz = 103
kHz).
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3.22
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.
Note
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3.23
If a signal does not change at all, itsfrequency is zero (for example, DC)
If a signal changes instantaneously, its
frequency is infinite (like the sharp
vertical edge of a pulse) .
Note
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3.24
Phase describes the position of thewaveform relative to time 0.
Note
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3.25
Figure 3.6 Three sine waves with the same ampl itude and f requency,but di fferent phases
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3.26
A sine wave is offset 1/6 cycle with respect to time 0.What is its phase in degrees and radians?
Example 3.6
SolutionWe know that 1 complete cycle is 360. Therefore, 1/6
cycle is
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3.27
Figure 3.7 Wavelength and period
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3.28
Figure 3.8 The time-domain and frequency-domain plots of a sine wave
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3.29
A complete sine wave in the timedomain can be represented by one
single spike in the frequency domain.
Note
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3.30
Th e f r eq u en c y d o m ain is m o re c o m p ac t an d
u s e f u l w h e n w e a r e d e a l i n g w i t h m o r e t h a n o n e
s i n e w a v e . F o r e x a m p l e , F i g u r e 3 . 8 s h o w s t h r e e
s in e w av es , eac h w i th d i ff er en t am p l it u d e an d
f r eq uen cy. A ll c an b e r ep res en ted b y t h ree
s p i k es i n t h e fr eq u en c y d o m ai n .
Example 3.7
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3.31
Figure 3.9 The time domain and frequency domain of three sine waves
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3.32
A single-frequency sine wave is notuseful in data communications;
we need to send a composite signal, a
signal made of many simple sine waves.
Note
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3.34
If the composite signal is periodic, the
decomposition gives a series of signals
with discrete frequencies;
if the composite signal is nonperiodic,
the decomposition gives a combination
of sine waves with continuousfrequencies.
Note
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3.35
Figure 3.10 shows a periodic composite signal withfrequency f. This type of signal is not typical of those
found in data communications. We can consider it to be
three alarm systems, each with a different f requency.
The analysis of this signal can give us a good
understanding of how to decompose signals.
Example 3.8
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Fi 3 11
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3.37
Figure 3.11 Decomposition of a composite per iodic signal in the time andfrequency domains
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3.38
F igure 3.12 shows a nonper iodic composite signal. I tcan be the signal created by a microphone or a telephone
set when a word or two is pronounced. I n this case, the
composite signal cannot be per iodic, because that
implies that we are repeating the same word or words
with exactly the same tone.
Example 3.9
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3.39
Figure 3.12 The time and f requency domains of a nonper iodic signal
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3.41
Figure 3.13 The bandwidth of per iodic and nonperiodic composite signals
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3.43
Figure 3.13 The bandwidth of per iodic and nonperiodic composite signals
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3.44
Figure 3.14 The bandwidth for Example 3.10
E l 3 11
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3.45
A periodic signal has a bandwidth of 20 Hz. The highestfrequency is 60 Hz. What is the lowest f requency? Draw
the spectrum if the signal contains all frequencies of the
same ampli tude.
SolutionLetfhbe the highest f requency,flthe lowest frequency,
andBthe bandwidth. Then
Example 3.11
The spectrum contains all integer frequencies. We show
this by a ser ies of spikes (see F igure 3.14).
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3.46
Figure 3.15 The bandwidth for Example 3.11
E l 3 12
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3.47
A nonper iodic composite signal has a bandwidth of 200kH z, with a middle frequency of 140 kH z and peak
amplitude of 20 V. The two extreme frequencies have an
amplitude of 0. Draw the frequency domain of the
signal.
Solution
The lowest f requency must be at 40 kHz and the highest
at 240 kHz. F igure 3.15 shows the frequency domain
and the bandwidth.
Example 3.12
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3.48
Figure 3.16 The bandwidth for Example 3.12
E l 3 13
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3.49
An example of a nonper iodic composite signal is thesignal propagated by an AM radio station. I n the United
States, each AM radio station is assigned a 10-kHz
bandwidth. The total bandwidth dedicated to AM radio
ranges from 530 to 1700 kHz. We wil l show the rationalebehind this 10-kH z bandwidth in Chapter 5.
Example 3.13
E l 3 14
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3.50
Another example of a nonper iodic composite signal isthe signal propagated by an FM radio station. In the
United States, each FM radio station is assigned a 200-
kHz bandwidth. The total bandwidth dedicated to FM
radio ranges from 88 to 108 MHz. We wil l show the
rationale behind this 200-kHz bandwidth in Chapter 5.
Example 3.14
E l 3 15
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3.51
Another example of a nonper iodic composite signal isthe signal received by an old-fashioned analog black-
and-white TV. A TV screen is made up of pixels. I f we
assume a resolution of 525 700, we have 367,500
pixels per screen. I f we scan the screen 30 times persecond, this is 367,500 30 = 11,025,000 pixels per
second. The worst-case scenario is alternating black and
white pixels. We can send 2 pixels per cycle. Therefore,
we need 11,025,000 / 2 = 5,512,500 cycles per second, orHz. The bandwidth needed is 5.5125 MHz.
Example 3.15
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3.52
L isten to Waveforms
http: //www.jhu.edu/~signals/l isten-new/listen-newindex.htm
http://www.jhu.edu/~signals/listen-new/listen-newindex.htmhttp://www.jhu.edu/~signals/listen-new/listen-newindex.htmhttp://www.jhu.edu/~signals/listen-new/listen-newindex.htm8/13/2019 Ch03 Part1 Modified SP2014
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3.53
Four ier Seri es Demo
http://www.falstad.com/fourier/
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Tw=1 msec, 1/Tw =1kHz, Tp=2 msec, 1/Tp=5kH z
Envelope zeros @ mul tiple integers of 2/Tw, peaks @ multiple integers of 1/Tw
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periodic
discrete spectral components
Peri od = 5 msec (peaks)