transmission media. quiz: angel->lessons->quiz 2 figure 1figure 2 figure 3figure 4
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Reading for next class Ch. 8.1 – 8.12TRANSCRIPT
Transmission Media
Quiz: ANGEL->Lessons->Quiz 2
Figure 1 Figure 2
Figure 3 Figure 4
Reading for next class
• Ch. 8.1 – 8.12
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Review: Bandwidth of a digital signal•The bandwidth of a digital signal is infinite!
– Accurate representation of a digital signal requires an infinite set of sine waves.
– Transmitting/reproducing digital signals is impractical
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Review: Bandwidth-Limited Signals•The bandwidth of a digital signal is infinite!
– Accurate representation of a digital signal requires an infinite set of sine waves.
– Transmitting/reproducing digital signals is impractical
•Engineers adopt a compromise: – generate composite sine waves that closely
approximate the digital signal– the quality of approximation depends on the channel
bandwidth
Review: Bandwidth-Limited Signals
• Having less bandwidth degrades the signal8 sine waves
4 sine waves
2 sine waves
Lost!
Bandwidth
Lost!
Lost!
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Receiver: Converting an Analog Signal back to Digital
1. (Sampling) The level of analog signal is measured repeatedly at fixed time intervals
2. (Quantization) A sample is then quantized by converting it into an integer value…
How many samples do we need?
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• too few samples: may only give a crude approximation of the original signal
• too many samples: more digital data will be generated, which uses extra bandwidth
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The Nyquist Theorem and Sampling Rate
• A mathematician named Nyquist discovered exactly how much sampling is required:
– fmax : the highest frequency in the composite signal.
• Sample a signal at least twice as fast as the highest frequency that must be preserved.
Example: At what rate should we sample this signal?
• Maximum frequency = 2Hz• Sampling rate: 2*2Hz = 4Hz
Exercise
• Q: At what rate should we sample the following signal?
Bandwidth to Channel Capacity
• In practice, the maximum frequency of a signal is determined by the channel bandwidth B.– Nyquist Theorem: maximum symbol rate (baud) is 2B
• Thus, if there are K signal levels, ignoring noise, the maximum bit rate is:
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Example: Bit Rate of Telephone System
• Audio bandwidth– Acceptable quality: preserving frequency up to 4k– Sampling rate (baud) = 2*4K = 8K
• Quantization:– Reasonable quality reproduction: 8 bits / 256 levels
Exercise
• If 8 signal levels are used, what is the data rate that can be sent over a coaxial cable that has an analog bandwidth of 6.2 MHz?
A Taxonomy of Transmission Media by Forms of Energy
.
wired
Twisted Pair, Coaxial Cable, or Optical Fiber?
Figure 1 Figure 2
Figure 3 Figure 4
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Copper (Electrical) Wiring vs. Optical Fiber
• Copper– Less expensive– No need special treatment on wires
• Ends of an optical fiber must be polished before being used.– Installation is easy. – Less likely to break if accidentally pulled or bent
• Optical fiber– Immune to electrical noise– Higher bandwidth– Light traveling across a fiber does not attenuate as much as
electrical signals traveling across copper.
How fast can we send information over a channel with noise?
• Key channel properties: The bandwidth (B), single strength (S), and noise strength (N)– B limits the rate of transmissions– S and N limit how many signal levels we can
distinguish
Bandwidth B Signal S,Noise N
The Effect of Noise on Communication
• In practice, the signal levels we can distinguish depends on S/N– Or SNR, the Signal-to-Noise Ratio
• Shannon’s Theorem
Example
• If a system has an average power level of 100, an average noise level of 33.33, and a bandwidth of 100 MHz, what is the effective limit on channel capacity?
Calculate Channel Capacity with S/N in dB • SNR often given on a log-scale in deciBels:
• Example: the voice telephone system:– Signal-to-noise ratio: about 30 dB– An analog bandwidth: about 3 kHz
• Calculation– Step 1: Converting the S/N in dB into a simple fraction: S/N = 10(dB/10)
• 30dB 1000– Step 2: Applying Shannon's Theorem
about 30,000 bps
dB = 10log10(S/N)
Exercise
• If a telephone system can be created with a signal-to-noise ratio of 40 dB and an analog bandwidth of 3000 Hz, how many bits per second could be transmitted?