CS412 Introduction to Computer Networking

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CS412 Introduction to Computer Networking
Telecommunication

• Theoretical Basis of
• Data Communication

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Topics

• Analog/Digital Signals
• Time and Frequency Domains
• Bandwidth and Channel Capacity
• Data Communication Measurements

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Signals

• Information must be transformed into
  electromagnetic signals to be transmitted
• Signal forms
• Analog or digital
• Periodic or aperiodic

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Analog/Digital Signals

• Analog signal
• Continuous waveform
• Can have a infinite number of values in a range
• Digital signal
• Discrete
• Can have only a limited number of values
• E.g., 0 or 1

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Figure 3.1 Comparison of analog and digital
signals
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Periodic/Aperiodic Signals

• Periodical signal
• Contains continuously repeated pattern
• Period (T) amount of time needed for the pattern
  to complete
• Aperiodical signal
• Contains no repetitive signals

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Analog Signals

• Simple analog signal
• Sine wave
• 3 characteristics
• 1. Peak amplitude (A)
• 2. Frequency (f)
• 3. Phase (?)
• Composite analog signal
• Composed of multiple sine waves

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Figure 3.2 A sine wave
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Figure 3.3 Amplitude
s(t) instantaneous amplitude
t
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Characteristics of Analog Signal

• Peak amplitude highest intensity
• Frequency (f)
• Number of cycles/rate of change per second
• Measured in Hertz (Hz), KHz, MHz, GHz,
• Period (T) amount of time it takes to complete
  one cycle
• f 1/T
• Phase position of the waveform relative to time 0

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Figure 3.4 Period and frequency
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Table 3.1 Units of periods and frequencies
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Figure 3.5 Relationships between different
phases
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Figure 3.6 Sine wave examples
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Figure 3.6 Sine wave examples (continued)
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Figure 3.6 Sine wave examples (continued)
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Characteristics of Analog Signal

• Changes in the three characteristics provides the
  basis for telecommunication
• Used by modems (later )

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Time Vs. Frequency Domain

• The sine waves shown previously are plotted in
  its time domain.
• An analog signal is best represented in the
  frequency domain.

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Figure 3.7 Time and frequency domains
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Composite Signals

• A composite signal can be decomposed into
  component sine waves - harmonics
• The decomposition is performed by Fourier Analysis

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Figure 4-13
Signal with DC Component
? The McGraw-Hill Companies, Inc., 1998
WCB/McGraw-Hill
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Figure 3.8-3.10 Square wave and the first
three harmonics
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Figure 3.11 Frequency spectrum comparison
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Frequency Spectrum and Bandwidth

• Frequency spectrum
• Collection of all component frequencies it
  contains
• Bandwidth
• Width of frequency spectrum

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Figure 3.13 Bandwidth
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Example 3
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
B fh - fl 900 - 100 800 Hz The spectrum
has only five spikes, at 100, 300, 500, 700, and
900 (see Figure 13.4 )
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Figure 3.14 Example 3
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Example 4
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
B fh - fl 20 60 - fl fl 60 - 20 40 Hz
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Figure 3.15 Example 4
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Example 5
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
The answer is definitely no. Although the signal
can have the same bandwidth (1000 Hz), the range
does not overlap. The medium can only pass the
frequencies between 3000 and 4000 Hz the signal
is totally lost.
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Digital Signals

• 0s and 1s
• Bit interval and bit rate
• Bit interval time required to send 1 bit
• Bit rate bit intervals in one second

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Example 6
A digital signal has a bit rate of 2000 bps. What
is the duration of each bit (bit interval)
Solution
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
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Digital Signal - Decomposition

• A digital signal can be decomposed into an
  infinite number of simple sine waves (harmonics),
  each with a different amplitude, frequency, and
  phase
• ?A digital signal is a composite signal with an
  infinite bandwidth.
• Significant spectrum
• Components required to reconstruct the digital
  signal

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Figure 4-20
Harmonics of a Digital Signal
? The McGraw-Hill Companies, Inc., 1998
WCB/McGraw-Hill
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Bandwidth-Limited Signals

• (a) A binary signal and its root-mean-square
  Fourier amplitudes.

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Bandwidth-Limited Signals (2)

• (b) (e) Successive approximations to the
  original signal.

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Figure 4-21
Exact and Significant Spectrums
? The McGraw-Hill Companies, Inc., 1998
WCB/McGraw-Hill
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Channel Capacity

• Channel capacity
• Max. bit rate a transmission medium can transfer
• Nyquist theorem
• C 2H log2V
• where C channel capacity (bit per second)
• H bandwidth (Hz)
• V signal levels (2 for binary)
• C is proportional to H
• ? Significant bandwidth puts a limit on channel
  capacity

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Figure 3.18 Digital versus analog
To transmit 6bps, we need a bandwidth 3 - 0
3Hz
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Channel Capacity

• Nyquist theorem is for noiseless (error-free)
  channels.
• Shannon Capacity
• C H log2(1 S/N)
• where C (noisy) channel capacity (bps)
• H bandwidth (Hz)
• S/N signal-to-noise ratio
• dB 10 log10 S/N
• In practice, we have to apply both for
  determining the channel capacity.

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Example 7
Consider a noiseless channel with a bandwidth of
3000 Hz transmitting a signal with two signal
levels. The maximum bit rate can be calculated as
Bit Rate 2 ? 3000 ? log2 2 6000 bps
Example 8
Consider the same noiseless channel, transmitting
a signal with four signal levels (for each level,
we send two bits). The maximum bit rate can be
calculated as
Bit Rate 2 x 3000 x log2 4 12,000
bps
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Example 9
Consider an extremely noisy channel in which the
value of the signal-to-noise ratio is almost
zero. In other words, the noise is so strong that
the signal is faint. For this channel the
capacity is calculated as
C B log2 (1 S/N) B log2 (1 0) B log2
(1) B ? 0 0
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Example 10
We can calculate the theoretical highest bit rate
of a regular telephone line. A telephone line
normally has a bandwidth of 3000 Hz (300 Hz to
3300 Hz). The signal-to-noise ratio is usually
35dB, i.e., 3162. For this channel the capacity
is calculated as
C B log2 (1 S/N) 3000 log2 (1 3162)
3000 log2 (3163) C 3000 ? 11.62 34,860 bps
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Example 11
We have a channel with a 1 MHz bandwidth. The S/N
for this channel is 63 what is the appropriate
bit rate and signal level?
Solution
First, we use the Shannon formula to find our
upper limit.
C B log2 (1 S/N) 106 log2 (1 63) 106
log2 (64) 6 Mbps
Then we use the Nyquist formula to find the
number of signal levels.
4 Mbps 2 ? 1 MHz ? log2 L ? L 4
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Data Communication Measurements

• Throughput
• How fast data can pass through an entity
• Propagation speed
• Depends on medium and signal frequency
• Propagation time (propagation delay)
• Time required for one bit to travel from one
  point to another
• Wavelength
• Propagation speed wavelength X frequency

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Figure 3.25 Throughput
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Figure 3.26 Propagation time
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Figure 3.27 Wavelength