Chi-Cheng Lin, Winona State University

Topics
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Data Communication Performance
Measurements

Analog/Digital Signals

Time and Frequency Domains

Bandwidth and Channel Capacity
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Data Communication Performance
Measurements


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Throughput
 How fast data can pass through an entity
 Number of bits passing through an a second imaginary wall in
Bit time
 Duration of a bit (time for a bit ejected into network)
 1 / throughput
Propagation time (propagation delay)
 Time required for one bit to travel from one point to another
 Propagation speed depends on medium and signal frequency
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Message Transmission Delay
Total transmission delay
= (size_of_message / throughput) + propagation_time
Sender 01101… Time
Receiver t
0 first bit sent t
1 last bit sent propagation_time t
01101…
2 first bit arrived t
3 last bit arrived
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Message Transmission Delay - Example


What is the transmission delay of a 2 KB message transmitted over a 2 km cable that has a throughput
40 Mbps and a propagation delay of 8 µs/km?
Answer:
Total transmission delay
= (size_of_message / throughput) + propagation_time
= (2048 x 8 bits / 40x10 6 bits/sec) + 8 µs/km x 2 km
= 409.6 x 10 -6 sec + 16 µs
= 425.6 µs
What is the bit time?
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Signals


Information must be transformed into electromagnetic signals to be transmitted
Signal forms
 Analog or digital
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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 and 1, i.e., two levels, for binary signal
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Time Vs. Frequency Domain

A signal can be represented in either the time domain.
domain or the frequency
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Period (Time) and Frequency
Unit
Seconds (s)
Equivalent
1 s
Unit
Hertz (Hz)
Milliseconds (ms) 10 –3 s Kilohertz (KHz)
Microseconds (ms) 10 –6 s Megahertz (MHz)
Nanoseconds (ns)
Picoseconds (ps)
10
10
–9
–12 s s
Gigahertz (GHz)
Terahertz (THz)
Equivalent
1 Hz
10 3 Hz
10 6 Hz
10 9 Hz
10 12 Hz
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Composite Signals
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A composite signal can be decomposed into component sine waves harmonics
The decomposition is performed by
Fourier Analysis
DC component is the one with frequency 0.
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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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Digital Signal - Decomposition


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A digital signal can be decomposed into an infinite number of simple sine waves
(harmonics)
 A digital signal is a composite signal with an infinite bandwidth.
More harmonics components
= better approximation
 Animation
Significant spectrum
 Components required to reconstruct the digital signal
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
Bandwidth-Limited Signals
(a) A binary signal and its root-meansquare Fourier amplitudes.
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Bandwidth-Limited Signals (2)

(b) – (e) Successive approximations to the original signal.
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
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Channel Capacity
Channel capacity
 Maximum bit rate a transmission medium can transfer
Nyquist theorem for noiseless channels
 C = 2 H where log
2
V
C : channel capacity (bit per second)
H : bandwidth (Hz)
V : signal levels (2 for binary)
 C is proportional to H
 bandwidth puts a limit on channel capacity
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Channel Capacity


Shannon Capacity for noisy channels
 C = H where log
2
(1 + S/N )
C : (noisy) channel capacity (bps)
H : bandwidth (Hz)
S/N : signal-to-noise ratio dB = 10 log
10
S/N
In practice, we have to apply both for determining the channel capacity.
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
Examples
Noiseless channel.
Consider a noiseless channel with a bandwidth of 3000 Hz transmitting a signal with two signal levels. What is the maximum bit rate of this channel?
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Noiseless channel.
Consider the same noiseless channel, transmitting a signal with four signal levels (for each level, we send two bits). What is the maximum bit rate of this channel?
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Extremely noisy channel.
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. What is the channel capacity of this channel?
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Examples

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. What is the capacity of this channel?

Applying both theorems.
We have a channel with a 2 MHz bandwidth. The S/N for this channel is 127; what is the appropriate bit rate and signal level?
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