1. CHAPTER 3 DATA AND SIGNAL
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2. Position of The Physical Layer
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3. Duties of Physical Layer
Bit-signal transformation
Bit-rate control
Bit synchronization
Bandwidth utilization: Multiplexing
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4. Data & Signal Data Entities that convey meaning
To be transmitted, data must be
transformed to electromagnetic signals.
Signal
Electric or electromagnetic representations of data
means by which data are propagated
Transmission
Communication of data by propagation
and processing of signals
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5. Analog and Digital Data
Analog data refers to information that is continuous
e.g human voice, video
Analog Data
Digital refers to information that has discrete states
e.g. data stored in the memory of computer in the form of 0s and 1s
Digital Data
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6. Analog and Digital Signals
can have an infinite number of values in a range
Analog signals
can have only a limited number of values
Digital signals
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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7. Comparison of Analog and Digital Signal
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8. Periodic and Nonperiodic Signals
Both analog and digital signals can be in two forms;
In data communications, we commonly use periodic analog signals and nonperiodic digital signals
Periodic signals
consists of continuous repetitive pattern within a time frame called period
the completion of one full pattern is called cycle
Nonperiodic signals (aperiodic)
has no repetitive pattern
can be decomposed into infinite number of periodic signals
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9. Periodic Signals
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10. Nonperiodic Signals
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11. 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:
Peak amplitude (A)
Frequency (f)
Phase (ø)
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12. Sine Wave Signal
S(t) = A sin (2  f t +  )
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13. Sine Wave: Peak amplitude (A)
The value of its highest intensity, proportional to the energy it carries
Measured by volts
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14. Sine Wave: Peak amplitude (A)
Two signals with the same phase and frequency, but different amplitudes
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15. 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
T= and f = 1
f T
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16. Sine Wave: Frequency ( f )
Two signals with the same amplitude and phase, but different frequencies
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17. 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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18. Units of Period and Frequency
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19. Example 1: Express a period of 100 ms in microseconds. Solution
We make the following substitutions:
100 ms = 100  10-3 s = 102  10-3  106 μs = 105 μs
1 ms = 10-3 s
1 s = 106 μs
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20. Example 2:
A period of signals is100 ms. Express the corresponding frequency in kilohertz.
Solution
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
T= and f = 1
f T
1 ms = 10-3 s
1 Hz = 10-3 kHz
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21. Example 3: Express a period of 1,000,000 μs in second. Solution
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22. Example 4:
A period of signals is 1,000,000 μs. Express the corresponding frequency in kilohertz.
Solution
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23. 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?
Solution
T = 1 = = s = x ms = ms f
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24. 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?
Solution
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25. Sine Wave : Phase (ø) Phase (ø)
Described the position of the waveform relative to time zero
Measured in degrees or radians:
360° = 2π rad
1° = 2π/360 rad
1 rad = 360/(2π)
Four types of phase: 0°
90°
180°
270°
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26. Sine Wave : Phase (ø)
Phase change
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27. Sine Wave : Phase (ø)
Four sine waves with the same amplitude and frequency, but different phases
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28. 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? Solution 1) Phase in degree: One complete cycle is 360 degrees. Therefore, 1/6 cycle: 2) Phase in radians: 1° is 2π/360 rad. Therefore, 60° :
1 x 360 = 60° 6
60 ° x 2π rad = π = rad
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29. Example 8:
A sine wave is offset 1/8 cycle with respect to time 0. What is its phase in degrees and radians? Solution 1) Phase in degree: 2) Phase in radians:
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30. Example 9:
A sine wave is offset 3/4 cycle with respect to time 0. What is its phase in degrees and radians? Solution 1) Phase in degree: 2) Phase in radians:
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31. 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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32. Wavelength= propagation speed x period= propagation speed
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 = λ micrometers or microns
propagation speed = c
frequency = f
c = 3*108 m/s
Wavelength= propagation speed x period= propagation speed
frequency
λ = ct or λ = c d f
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33. Example 10: λ = c = 3*108 8= 0.75 * 10-6 m = 0.75 microns
Calculate the wavelength of red light if its frequency is 4 x 1014 Solution
λ = c d f
λ = c = 3* = 0.75 * 10-6 m = 0.75 microns
f x 1014
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34. 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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35. Sine Wave: Time & Frequency Domain
Time and frequency domains
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36. 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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37. 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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38. 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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39. 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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40. A composite periodic signal
Composite Signals
A composite periodic signal
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41. Decomposition of a composite periodic signal in the time and
Composite Signals
Decomposition of a composite periodic signal in the time and
frequency domains
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42. 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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43. The time and frequency domains of a nonperiodic signal
Composite Signals
The time and frequency domains of a nonperiodic signal
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44. 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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45. Bandwidth (B)
Bandwidth
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46. 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. Solution Bandwidth: B = fh - fl = = 800 Hz The spectrum has only five spikes, at 100, 300, 500, 700, and 900 (see Figure 3.9 )
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47. The bandwidth for 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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48. 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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49. Example 11: Bandwidth spectrum:
The spectrum has only five spikes, at 100, 300, 500, 700, and 900.
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50. 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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51. Exercises
Given the frequencies listed below, calculate the corresponding periods.
8 MHz
140KHz
Given the following periods, calculate the corresponding frequencies.
5 s
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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52. 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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