Transcript CHAPTER 3

CHAPTER 3
DATA AND SIGNAL
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Position of The Physical Layer
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Duties of Physical Layer
Bit-signal
transformation
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Bit
synchronization
Bit-rate control
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Bandwidth
utilization:
Multiplexing
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Data & Signal
Data
Signal
Transmission
• Entities that
convey
meaning
• To be
transmitted,
data must be
• transformed to
electromagnetic
signals.
• Electric or
electromagnetic
representations
of data
• means by which
data are
propagated
• Communication
of data by
propagation
• and processing
of signals
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Analog and Digital Data
• Analog data refers to
information that is
continuous
• Digital refers to
information that has
discrete states
• e.g human voice, video
• e.g. data stored in the
memory of computer in
the form of 0s and 1s
Analog Data
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Digital Data
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Analog and Digital Signals
Analog signals
• can have an infinite number of
values in a range
Digital signals
• can have only a limited number
of values
The simplest way to show signals is by plotting them on a
pair of perpendicular axes:
-vertical axis represents the value or strength of a signal
-horizontal axis represents time
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Comparison of Analog and Digital Signal
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Periodic and Nonperiodic Signals
• Both analog and digital signals can be in two forms;
Nonperiodic signals
(aperiodic)
Periodic signals
• consists of continuous
repetitive pattern within a
time frame called period
• the completion of one full
pattern is called cycle
• has no repetitive pattern
• can be decomposed into
infinite number of
periodic signals
• In data communications, we commonly use periodic analog
signals and nonperiodic digital signals
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Periodic Signals
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Nonperiodic Signals
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Periodic Analog Signals
•
Can be classified as simple or composite
•
A simple periodic analog signal:
a sine wave, cannot be decomposed into simpler signals
•
A composite periodic analog signal:
is composed of multiple sine waves
•
Sine wave can be described by three characteristics:
1.
2.
3.
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Peak amplitude (A)
Frequency (f)
Phase (ø)
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Sine Wave Signal
S(t) = A sin (2  f t +  )
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Sine Wave: Peak amplitude (A)
•
Peak amplitude (A)
– The value of its highest intensity, proportional to the
energy it carries
– Measured by volts
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Sine Wave: Peak amplitude (A)
Two signals with the same phase and frequency, but different amplitudes
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Sine Wave: Frequency ( f )
•
Period (T) and frequency (f)
– The amount of time (in seconds) needs to complete in
one cycle
– Period
= time for one repetition (T)
– Frequency (f) = the number of period in a second
(expressed in Hertz)
– Frequency and period are the inverse of each other
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Sine Wave: Frequency ( f )
Two signals with the same amplitude and phase, but different frequencies
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Sine Wave: Frequency ( f )
•
Frequency is the rate of change with respect to time.
- high frequency = change in a short span of time
- low frequency = change over a long span of time
- zero frequency = if a signal does not change at all
- infinite frequency= if a signal changes instantaneously
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Units of Period and Frequency
Units of period and frequency
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Example 1:
Express a period of 100 ms in microseconds.
1 ms = 10-3 s
1 s = 106 μs
We make the following substitutions:
100 ms = 100  10-3 s = 102  10-3  106 μs = 105 μs
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Example 2:
A period of signals is100 ms. Express the corresponding
frequency in kilohertz.
1 ms = 10-3 s
1 Hz = 10-3 kHz
First we change 100 ms to seconds
100 ms = 100  10-3 s = 102  10-3 s = 10-1 s
Then we calculate the frequency from the period
f = 1 Hz = 10 Hz = 10 x 10-3 kHz = 10-2 kHz
10-1
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Example 3:
Express a period of 1,000,000 μs in second.
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Example 4:
A period of signals is 1,000,000 μs. Express the corresponding
frequency in kilohertz.
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Example 5:
The power in your house (North America) can be represented by
a sine wave with a peak amplitude between 110 to 220 V.
The power we use at home (North America) has a frequency of
60 Hz. What is the period of this sine wave?
T =1
f
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= 1 = 0.0166 s = 0.0166 x 10-3 ms = 16.6 ms
60
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Example 6:
The power in your house (Malaysia) can be represented by a
sine wave with a peak amplitude between 220 to 240 V.
The power we use at home has a frequency of 50 Hz. What is
the period of this sine wave?
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Sine Wave : Phase (ø)
•
Phase (ø)
– Described the position of the waveform relative to time zero
–
Measured in degrees or radians:
•
•
•
–
= 2π rad
= 2π/360 rad
= 360/(2π)
Four types of phase:
•
•
•
•
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360°
1°
1 rad
0°
90°
180°
270°
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Sine Wave : Phase (ø)
Phase change
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Sine Wave : Phase (ø)
Four sine waves with the same amplitude and frequency, but different phases
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Example 7:
A sine wave is offset 1/6 of a cycle with respect to time 0. What is its
phase in degrees and radians?
1) Phase in degree:
One complete cycle is 360 degrees. Therefore, 1/6 cycle:
1 x 360 = 60°
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2) Phase in radians:
1° is 2π/360 rad. Therefore, 60° :
60 ° x 2π rad = π = 1.046 rad
360
3
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Example 8:
A sine wave is offset 1/8 cycle with respect to time 0. What is its phase in
degrees and radians?
1) Phase in degree:
2) Phase in radians:
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Example 9:
A sine wave is offset 3/4 cycle with respect to time 0. What is its phase in
degrees and radians?
1) Phase in degree:
2) Phase in radians:
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Sine Wave: Wavelength
• Distance occupied by one cycle
• Distance between two points of corresponding phase in two
consecutive cycles
• It binds the period of a sine wave to the propagation speed of
the medium
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Sine Wave: Wavelength
• Wavelength can be calculated if one is given the propagation
speed (the speed of light) and the period of the signal.
• However, since period and frequency are related to each
other, if we represent:
– wavelength
– propagation speed
– frequency
= λ micrometers or microns
= c c = 3*108 m/s
=f
Wavelength= propagation speed x period= propagation speed
frequency
λ = ct
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or
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λ= c d
f
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Example 10:
Calculate the wavelength of red light if its frequency is 4 x 1014
λ= c d
f
λ = c = 3*108 8= 0.75 * 10-6 m = 0.75 microns
f
4 x 1014
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Sine Wave: Time & Frequency Domain
•
Time and Frequency domain
– The time-domain plot shows changes in signal amplitude
with respect to time
– To show relationship between amplitude and frequency,
we use frequency domain plot
– An analog signal is best represented in the frequency
domain
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Sine Wave: Time & Frequency Domain
Time and frequency domains
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Sine Wave: Time & Frequency Domain
• The frequency domain is more compact and useful when we
are dealing with more than one sine wave.
– e.g: Figure below shows three sine waves, each with different amplitude
and frequency.
– All can be represented by three frequency spikes in the frequency
domain.
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Composite Signals
• A single-frequency sine wave is NOT useful in data
communications;
• We need to send a composite signal, a signal made of many
simple sine waves.
Fourier analysis
• any combination of simple sine waves with different
frequencies, amplitudes, and phases.
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Composite Signals
• 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
continuous frequencies
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Composite Signals
Example:
• Figure below shows a periodic composite signal with
frequency ( 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 frequency.
• The analysis of this signal can give us a good understanding
of how to decompose signals.
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Composite Signals
A composite periodic signal
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Composite Signals
Decomposition of a composite periodic signal in the time and
frequency domains
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Composite Signals
Example:
• Figure below shows a nonperiodic composite signal. It can be
the signal created by a microphone or a telephone set when a
word or two is pronounced.
• In this case, the composite signal cannot be periodic, because
that implies that we are repeating the same word or words
with exactly the same tone.
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Composite Signals
The time and frequency domains of a nonperiodic signal
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Bandwidth (B)
• The bandwidth of a composite signal is the difference
between the highest (fh) and the lowest (fl) frequencies
contained in that signal.
• The bandwidth of a medium:
– the difference between the highest (fh) and the lowest (fl)
frequencies that the medium can satisfactorily pass
B = fh - fl
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Bandwidth (B)
Bandwidth
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Example 10:
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.
Bandwidth:
B = fh - fl = 900 - 100 = 800 Hz
The spectrum has only five spikes, at 100, 300, 500, 700, and 900 (see
Figure 3.9 )
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Example 10:
Bandwidth spectrum:
The spectrum has only five spikes, at 100, 300, 500, 700, and 900.
The bandwidth for Example 10
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Example 11:
• 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.
Solution
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Example 11:
Bandwidth spectrum:
The spectrum has only five spikes, at 100, 300, 500, 700, and 900.
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Example 12:
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?
Solution
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Exercises
• Given the frequencies listed below, calculate the corresponding
periods.
a. 8 MHz
b. 140KHz
• Given the following periods, calculate the corresponding
frequencies.
a. 5 s
b. 220 ns
• What is the phase shift for the following?
a. A sine wave with the maximum amplitude at time zero
b. A sine wave with maximum amplitude after 1/4 cycle
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Exercises
• What is the bandwidth of a signal that can be decomposed into five
sine waves with frequencies at 0, 20, 50, 100, and 200 Hz? All peak
amplitudes are the same. Draw the bandwidth.
• A periodic composite signal with a bandwidth of 2000Hz is
composed of two sine waves. The first one has a frequency of 100
Hz with a maximum amplitude of 20 V; the second one has a
maximum amplitude of 5 V. Draw the bandwidth.
• Which signal has a wider bandwidth, a sine wave with a frequency
of I 00 Hz or a sine wave with a frequency of 200 Hz?
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